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Sample records for fast multipole boundary

  1. A new simple multidomain fast multipole boundary element method

    NASA Astrophysics Data System (ADS)

    Huang, S.; Liu, Y. J.

    2016-06-01

    A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM.

  2. A new simple multidomain fast multipole boundary element method

    NASA Astrophysics Data System (ADS)

    Huang, S.; Liu, Y. J.

    2016-09-01

    A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM.

  3. A fast multipole hybrid boundary node method for composite materials

    NASA Astrophysics Data System (ADS)

    Wang, Qiao; Miao, Yu; Zhu, Hongping

    2013-06-01

    This article presents a multi-domain fast multipole hybrid boundary node method for composite materials in 3D elasticity. The hybrid boundary node method (hybrid BNM) is a meshless method which only requires nodes constructed on the surface of a domain. The method is applied to 3D simulation of composite materials by a multi-domain solver and accelerated by the fast multipole method (FMM) in this paper. The preconditioned GMRES is employed to solve the final system equation and precondition techniques are discussed. The matrix-vector multiplication in each iteration is divided into smaller scale ones at the sub-domain level and then accelerated by FMM within individual sub-domains. The computed matrix-vector products at the sub-domain level are then combined according to the continuity conditions on the interfaces. The algorithm is implemented on a computer code written in C + +. Numerical results show that the technique is accurate and efficient.

  4. A fast multipole boundary element method for solving two-dimensional thermoelasticity problems

    NASA Astrophysics Data System (ADS)

    Liu, Y. J.; Li, Y. X.; Huang, S.

    2014-09-01

    A fast multipole boundary element method (BEM) for solving general uncoupled steady-state thermoelasticity problems in two dimensions is presented in this paper. The fast multipole BEM is developed to handle the thermal term in the thermoelasticity boundary integral equation involving temperature and heat flux distributions on the boundary of the problem domain. Fast multipole expansions, local expansions and related translations for the thermal term are derived using complex variables. Several numerical examples are presented to show the accuracy and effectiveness of the developed fast multipole BEM in calculating the displacement and stress fields for 2-D elastic bodies under various thermal loads, including thin structure domains that are difficult to mesh using the finite element method (FEM). The BEM results using constant elements are found to be accurate compared with the analytical solutions, and the accuracy of the BEM results is found to be comparable to that of the FEM with linear elements. In addition, the BEM offers the ease of use in generating the mesh for a thin structure domain or a domain with complicated geometry, such as a perforated plate with randomly distributed holes for which the FEM fails to provide an adequate mesh. These results clearly demonstrate the potential of the developed fast multipole BEM for solving 2-D thermoelasticity problems.

  5. A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems

    NASA Astrophysics Data System (ADS)

    Zheng, Chang-Jun; Chen, Hai-Bo; Chen, Lei-Lei

    2013-04-01

    This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/plane-symmetric acoustic wave problems. The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only. Moreover, a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived, and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating, translating and saving the multipole/local expansion coefficients of the image domain. The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems. As for exterior acoustic problems, the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Details on the implementation of the present method are described, and numerical examples are given to demonstrate its accuracy and efficiency.

  6. Thermal analysis of 3D composites by a new fast multipole hybrid boundary node method

    NASA Astrophysics Data System (ADS)

    Miao, Yu; Wang, Qiao; Zhu, Hongping; Li, Yinping

    2014-01-01

    This paper applies the hybrid boundary node method (Hybrid BNM) for the thermal analysis of 3D composites. A new formulation is derived for the inclusion-based composites. In the new formulation, the unknowns of the interfaces are assembled only once in the final system equation, which can reduce nearly one half of degrees of freedom (DOFs) compared with the conventional multi-domain solver when there are lots of inclusions. A new version of the fast multipole method (FMM) is also coupled with the new formulation and the technique is applied to thermal analysis of composites with many inclusions. In the new fast multipole hybrid boundary node method (FM-HBNM), a diagonal form for translation operators is used and the method presented can be applied to the computation of more than 1,000,000 DOFs on a personal computer. Numerical examples are presented to analyze the thermal behavior of composites with many inclusions.

  7. A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation.

    PubMed

    Gumerov, Nail A; Duraiswami, Ramani

    2009-01-01

    The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations. PMID:19173406

  8. Dynamics of ULVZ-mantle interaction using fast multipole boundary element method

    NASA Astrophysics Data System (ADS)

    Drombosky, T.; Hier-Majumder, S.

    2012-12-01

    Seismic observations over the past two decades show evidence of areas immediately above the core-mantle boundary characterized by sharp, differential drops in seismic velocities. These aptly named UltraLow Velocity Zones (ULVZs) are typically localized (50-100km wide) and thin (10-40 km thick). High concentration of the observed ULVZ patches near the edges of Large Low Shear Velocity Provinces (LLSVPs) indicate that the shape and distribution of the dynamic ULVZ patches are strongly coupled with the flow in the adjacent mantle. Two important properties modulating the extent of this coupling are the contrasts in density and viscosity between the ULVZ patches and the surrounding mantle. This work explores the interaction, coalescence, and break-up of ULVZ patches excited by an imposed mantle flow using the Fast Multipole Boundary Element Method (FMBEM). We model the ambient mantle as a high viscosity medium containing viscous, deformable ULVZ patches. The ambient mantle and ULVZ patches are both homogeneous but may differ from each other in viscosity and density. Mass and momentum conservation within each patch and the mantle are governed by the Stokes flow equation. The governing partial differential equations, aided with stress jump and no-slip boundary conditions at the ULVZ-mantle interfaces, are converted into a set of Fredholm integral equations of the second kind. Unlike traditional Boundary Element Methods (BEM), discretization of this integral equation using FMBEM produces a system of linear equations solvable by iterative sparse solver methods. This work reports a set of numerical experiments over a range of viscosity and density contrasts.

  9. An Adaptive Fast Multipole Boundary Element Method for Poisson-Boltzmann Electrostatics

    SciTech Connect

    Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, Jonathan

    2009-01-01

    The numerical solution of the Poisson Boltzmann (PB) equation is a useful but a computationally demanding tool for studying electrostatic solvation effects in chemical and biomolecular systems. Recently, we have described a boundary integral equation-based PB solver accelerated by a new version of the fast multipole method (FMM). The overall algorithm shows an order N complexity in both the computational cost and memory usage. Here, we present an updated version of the solver by using an adaptive FMM for accelerating the convolution type matrix-vector multiplications. The adaptive algorithm, when compared to our previous nonadaptive one, not only significantly improves the performance of the overall memory usage but also remarkably speeds the calculation because of an improved load balancing between the local- and far-field calculations. We have also implemented a node-patch discretization scheme that leads to a reduction of unknowns by a factor of 2 relative to the constant element method without sacrificing accuracy. As a result of these improvements, the new solver makes the PB calculation truly feasible for large-scale biomolecular systems such as a 30S ribosome molecule even on a typical 2008 desktop computer.

  10. GPU-accelerated indirect boundary element method for voxel model analyses with fast multipole method

    NASA Astrophysics Data System (ADS)

    Hamada, Shoji

    2011-05-01

    An indirect boundary element method (BEM) that uses the fast multipole method (FMM) was accelerated using graphics processing units (GPUs) to reduce the time required to calculate a three-dimensional electrostatic field. The BEM is designed to handle cubic voxel models and is specialized to consider square voxel walls as boundary surface elements. The FMM handles the interactions among the surface charge elements and directly outputs surface integrals of the fields over each individual element. The CPU code was originally developed for field analysis in human voxel models derived from anatomical images. FMM processes are programmed using the NVIDIA Compute Unified Device Architecture (CUDA) with double-precision floating-point arithmetic on the basis of a shared pseudocode template. The electric field induced by DC-current application between two electrodes is calculated for two models with 499,629 (model 1) and 1,458,813 (model 2) surface elements. The calculation times were measured with a four-GPU configuration (two NVIDIA GTX295 cards) with four CPU cores (an Intel Core i7-975 processor). The times required by a linear system solver are 31 s and 186 s for models 1 and 2, respectively. The speed-up ratios of the FMM range from 5.9 to 8.2 for model 1 and from 5.0 to 5.6 for model 2. The calculation speed for element-interaction in this BEM analysis was comparable to that of particle-interaction using FMM on a GPU.

  11. A pragmatic overview of fast multipole methods

    SciTech Connect

    Strickland, J.H.; Baty, R.S.

    1995-12-01

    A number of physics problems can be modeled by a set of N elements which have pair-wise interactions with one another. A direct solution technique requires computational effort which is O(N{sup 2}). Fast multipole methods (FMM) have been widely used in recent years to obtain solutions to these problems requiring a computational effort of only 0 (N lnN) or O (N). In this paper we present an overview of several variations of the fast multipole method along with examples of its use in solving a variety of physical problems.

  12. An overview of fast multipole methods

    SciTech Connect

    Strickland, J.H.; Baty, R.S.

    1995-11-01

    A number of physics problems may be cast in terms of Hilbert-Schmidt integral equations. In many cases, the integrals tend to be zero over a large portion of the domain of interest. All of the information is contained in compact regions of the domain which renders their use very attractive from the standpoint of efficient numerical computation. Discrete representation of these integrals leads to a system of N elements which have pair-wise interactions with one another. A direct solution technique requires computational effort which is O(N{sup 2}). Fast multipole methods (FMM) have been widely used in recent years to obtain solutions to these problems requiring a computational effort of only O(Nln N) or O(N). In this paper we present an overview of several variations of the fast multipole method along with examples of its use in solving a variety of physical problems.

  13. Efficient Displacement Discontinuity Method Using Fast Multipole Techniques

    SciTech Connect

    Morris, J.P.; Blair, S.C.

    2000-02-18

    The Displacement Discontinuity method has been widely used in geomechanics because it accurately captures the behavior of fractures within a rock mass by explicitly accounting for discontinuities. Unfortunately, boundary element techniques require the interactions between all pairs of elements to be evaluated and traditional approaches to the Displacement Discontinuity method are computationally expensive for large problem sizes. Approximate summation techniques, such as the Fast Multipole Method (FMM), calculate the interactions between N entities in time proportional to N. We have implemented a modified Fast Multipole approach which performs the necessary calculations in optimal time and with reduced memory usage. Furthermore, the FMM introduces parameters which can be selected to give the desired trade-off between efficiency and accuracy. The FMM approach permits much larger problems to be solved using desktop computers, opening up a range of applications. We present results demonstrating the speed of the code and several test cases involving rock fracture in compression.

  14. Hierarchical Fast Multipole Simulation of Magnetic Colloids

    NASA Astrophysics Data System (ADS)

    Günal, Yüksel; Visscher, Pieter

    1997-03-01

    We have extended the well-known "fast multipole"footnote L. F. Greengard and V. Rokhlin, J. Comp. Phys. 73 p. 325, 1987. methods for molecular-dynamics simulation of large systems of point charges to continuum systems, such as magnetic films or particulate suspensions. (These methods reduce the computational labor from O(N^2) to O(N log N) or O(N), the number of particles). We apply the method to the particular case of a colloidal dispersion of magnetized cylindrical particles. Our method is fully hierarchical, both upward and downward from the particle size scale. The force on each particle is calculated by grouping distant particles into large clusters, nearer particles into smaller clusters, and dividing the nearest particles into segments. The fineness with which the particles are divided is controlled by an error tolerance parameter. The field of each cluster or segment is computed from a multipole expansion. Distant periodic images are also treated as multipoles - this is much faster than standard Fourier-transform or Ewald summation techniques.

  15. Fractional tiers in fast multipole method calculations

    NASA Astrophysics Data System (ADS)

    White, Christopher A.; Head-Gordon, Martin

    1996-08-01

    One defining characteristic of the fast multipole calculation is the number of tiers (depth of tree) used to group the particles. For three dimensions, the standard boxing scheme restricts the number of lowest level boxes to be a power of eight. We present a method which through a simple scaling of the particle coordinates allows an arbitrary number of lowest level boxes. Consequently, one can better balance the near-field and far-field work by minimizing the variation in the number of particles per lowest level box from its optimal value. Test calculations show systems where this method gives a speedup approaching two times.

  16. Fast multipole methods for particle dynamics

    PubMed Central

    Kurzak, J.; Pettitt, B. M.

    2008-01-01

    The growth of simulations of particle systems has been aided by advances in computer speed and algorithms. The adoption of O(N) algorithms to solve N-body simulation problems has been less rapid due to the fact that such scaling was only competitive for relatively large N. Our work seeks to find algorithmic modifications and practical implementations for intermediate values of N in typical use for molecular simulations. This article reviews fast multipole techniques for calculation of electrostatic interactions in molecular systems. The basic mathematics behind fast summations applied to long ranged forces is presented along with advanced techniques for accelerating the solution, including our most recent developments. The computational efficiency of the new methods facilitates both simulations of large systems as well as longer and therefore more realistic simulations of smaller systems. PMID:19194526

  17. A fast multipole transformation for global climate calculations

    SciTech Connect

    Holmes, J.A.; Wang, Z.; Drake, J.B.; Lyon, B.F.; Chen, W.T.

    1996-01-01

    A fast multipole transformation is adapted to the evaluation of summations that occur in global climate calculations when transforming between spatial and spherical harmonic representations. For each summation, the timing of the fast multipole transformation scales linearly with the number of latitude gridpoints, but the timing for direct evaluations scales quadratically. In spite of a larger computational overhead, this scaling advantage renders the fast multipole method faster than direct evaluation for transformations involving greater than approximately 300 to 500 gridpoints. Convergence of the fast multipole transformation is accurate to machine precision. As the resolution in global climate calculations continues to increase, an increasingly large fraction of the computational work involves the transformation between spatial and spherical harmonic representations. The fast multipole transformation offers a significant reduction in computational time for these high-resolution cases.

  18. Fast Multipole Methods for Particle Dynamics.

    SciTech Connect

    Kurzak, Jakub; Pettitt, Bernard M.

    2006-08-30

    The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. The growth of simulations of particle systems has been aided by advances in computer speed and algorithms. The adoption of O(N) algorithms to solve N-body simulation problems has been less rapid due to the fact that such scaling was only competitive for relatively large N. Our work seeks to find algorithmic modifications and practical implementations for intermediate values of N in typical use for molecular simulations. This article reviews fast multipole techniques for calculation of electrostatic interactions in molecular systems. The basic mathematics behind fast summations applied to long ranged forces is presented along with advanced techniques for accelerating the solution, including our most recent developments. The computational efficiency of the new methods facilitates both simulations of large systems as well as longer and therefore more realistic simulations of smaller systems.

  19. Three-dimensional nonplanar lithography simulation using a periodic fast multipole method

    NASA Astrophysics Data System (ADS)

    Yeung, Michael S.; Barouch, Eytan

    1997-07-01

    This paper discusses an extension of the fast multipole method to electromagnetic scattering from doubly periodic, multilayer wafer topography. The novelty of our approach lies in the use of a pseudo-periodic translation operator which can be computed efficiently using fast Fourier transform. Results obtained using the rigorous boundary conditions for dielectric surfaces are compared with those obtained using the approximate impedance boundary condition. The latter is shown to give good results for the type of topography usually encountered in lithography simulation. Results of reflective-notching simulation using the IBC method are presented.

  20. Electrical impedance tomography and the fast multipole method

    NASA Astrophysics Data System (ADS)

    Bikowski, Jutta; Mueller, Jennifer L.

    2004-10-01

    A 3-D linearization-based reconstruction algorithm for Electrical Impedance Tomography suitable for breast cancer detection using data collected on a rectangular array was introduced by Mueller et al. [IEEE Biomed. Eng., 46(11), 1999]. By considering the scenario as an electrostatic problem, it is possible to model the electrodes with various charges, facilitating the use of the Fast Multipole Method (FMM) for calculating particle interactions and also supporting the use of different electrode models. In this paper the use of FMM is explained and results in form of reconstructed images from experimental data show that this method is an improvement.

  1. AFMPB: An adaptive fast multipole Poisson Boltzmann solver for calculating electrostatics in biomolecular systems

    SciTech Connect

    Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, Jonathan

    2010-01-01

    A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage.

  2. Application of Fast Multipole Methods to the NASA Fast Scattering Code

    NASA Technical Reports Server (NTRS)

    Dunn, Mark H.; Tinetti, Ana F.

    2008-01-01

    The NASA Fast Scattering Code (FSC) is a versatile noise prediction program designed to conduct aeroacoustic noise reduction studies. The equivalent source method is used to solve an exterior Helmholtz boundary value problem with an impedance type boundary condition. The solution process in FSC v2.0 requires direct manipulation of a large, dense system of linear equations, limiting the applicability of the code to small scales and/or moderate excitation frequencies. Recent advances in the use of Fast Multipole Methods (FMM) for solving scattering problems, coupled with sparse linear algebra techniques, suggest that a substantial reduction in computer resource utilization over conventional solution approaches can be obtained. Implementation of the single level FMM (SLFMM) and a variant of the Conjugate Gradient Method (CGM) into the FSC is discussed in this paper. The culmination of this effort, FSC v3.0, was used to generate solutions for three configurations of interest. Benchmarking against previously obtained simulations indicate that a twenty-fold reduction in computational memory and up to a four-fold reduction in computer time have been achieved on a single processor.

  3. Object-Oriented Fast Multipole Simulation: Magnetic Colloids

    NASA Astrophysics Data System (ADS)

    Visscher, Pieter; Günal, Yüksel

    1997-08-01

    In simulating a system of N particles, if the interaction is long-ranged all pair interactions must be calculated, requiring CPU time of order N^2. Recently-developed ``fast multipole'' methods (FMM) can reduce this time to order N, at the cost of considerable programming complexity. We have developed an object-oriented approach which uses similar ideas but is conceptually much simpler. The system is represented by a hierarchical tree whose root is the entire system and whose lowest nodes are the particles. The entire calculation of the particle interactions consists of a single call to a recursive function CalculateInteractions(A,B) with A=B=root, which uses a simple opening-angle criterion to choose between multipole expansion and calling itself (subdividing A and B.) The resulting algorithm is essentially equivalent to the FMM, but the choice of when to subdivide (which is laboriously hard-wired in FMM) is made automatically. We will discuss the implementation of periodic BCs and the application of the method to continuum systems (cylindrical magnetic particles).

  4. Fast and accurate determination of the Wigner rotation matrices in the fast multipole method.

    PubMed

    Dachsel, Holger

    2006-04-14

    In the rotation based fast multipole method the accurate determination of the Wigner rotation matrices is essential. The combination of two recurrence relations and the control of the error accumulations allow a very precise determination of the Wigner rotation matrices. The recurrence formulas are simple, efficient, and numerically stable. The advantages over other recursions are documented. PMID:16626188

  5. A Massively Parallel Adaptive Fast Multipole Method on Heterogeneous Architectures

    SciTech Connect

    Lashuk, Ilya; Chandramowlishwaran, Aparna; Langston, Harper; Nguyen, Tuan-Anh; Sampath, Rahul S; Shringarpure, Aashay; Vuduc, Richard; Ying, Lexing; Zorin, Denis; Biros, George

    2012-01-01

    We describe a parallel fast multipole method (FMM) for highly nonuniform distributions of particles. We employ both distributed memory parallelism (via MPI) and shared memory parallelism (via OpenMP and GPU acceleration) to rapidly evaluate two-body nonoscillatory potentials in three dimensions on heterogeneous high performance computing architectures. We have performed scalability tests with up to 30 billion particles on 196,608 cores on the AMD/CRAY-based Jaguar system at ORNL. On a GPU-enabled system (NSF's Keeneland at Georgia Tech/ORNL), we observed 30x speedup over a single core CPU and 7x speedup over a multicore CPU implementation. By combining GPUs with MPI, we achieve less than 10 ns/particle and six digits of accuracy for a run with 48 million nonuniformly distributed particles on 192 GPUs.

  6. Communications overlapping in fast multipole particle dynamics methods

    SciTech Connect

    Kurzak, Jakub; Pettitt, B. Montgomery . E-mail: pettitt@uh.edu

    2005-03-01

    In molecular dynamics the fast multipole method (FMM) is an attractive alternative to Ewald summation for calculating electrostatic interactions due to the operation counts. However when applied to small particle systems and taken to many processors it has a high demand for interprocessor communication. In a distributed memory environment this demand severely limits applicability of the FMM to systems with O(10 K atoms). We present an algorithm that allows for fine grained overlap of communication and computation, while not sacrificing synchronization and determinism in the equations of motion. The method avoids contention in the communication subsystem making it feasible to use the FMM for smaller systems on larger numbers of processors. Our algorithm also facilitates application of multiple time stepping techniques within the FMM. We present scaling at a reasonably high level of accuracy compared with optimized Ewald methods.

  7. Communications Overlapping in Fast Multipole Particle Dynamics Methods

    SciTech Connect

    Kurzak, Jakub; Pettitt, Bernard M.

    2005-03-01

    The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. In molecular dynamics the fast multipole method (FMM) is an attractive alternative to Ewald summation for calculating electrostatic interactions due to the operation counts. However when applied to small particle systems and taken to many processors it has a high demand for interprocessor communication. In a distributed memory environment this demand severely limits applicability of the FMM to systems with O(10 K atoms). We present an algorithm that allows for fine grained overlap of communication and computation, while not sacrificing synchronization and determinism in the equations of motion. The method avoids contention in the communication subsystem making it feasible to use the FMM for smaller systems on larger numbers of processors. Our algorithm also facilitates application of multiple time stepping techniques within the FMM. We present scaling at a reasonably high level of accuracy compared with optimized Ewald methods.

  8. Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems.

    PubMed

    Fall, Mandiaye; Boutami, Salim; Glière, Alain; Stout, Brian; Hazart, Jerome

    2013-06-01

    A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations. PMID:24323115

  9. AFMPB: An adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems

    NASA Astrophysics Data System (ADS)

    Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew

    2013-11-01

    A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of the fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/lubz/afmpb.html for updates and changes. Running time: The running time varies with the number of discretized elements (N) in the system and their distributions. In most cases, it scales linearly as a function of N.

  10. Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

    NASA Astrophysics Data System (ADS)

    Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

    2015-11-01

    Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

  11. Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

    SciTech Connect

    Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

    2015-11-14

    Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

  12. A Fourier-series-based kernel-independent fast multipole method

    SciTech Connect

    Zhang Bo; Huang Jingfang; Pitsianis, Nikos P.; Sun Xiaobai

    2011-07-01

    We present in this paper a new kernel-independent fast multipole method (FMM), named as FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI-FMM creates, using numerical techniques, sufficiently accurate and compressive representations of a given kernel function over multi-scale interaction regions in the form of a truncated Fourier series. It provides also economic operators for the multipole-to-multipole, multipole-to-local, and local-to-local translations that are typical and essential in the FMM algorithms. The multipole-to-local translation operator, in particular, is readily diagonal and does not dominate in arithmetic operations. FKI-FMM provides an alternative and competitive option, among other kernel-independent FMM algorithms, for an efficient application of the FMM, especially for applications where the kernel function consists of multi-physics and multi-scale components as those arising in recent studies of biological systems. We present the complexity analysis and demonstrate with experimental results the FKI-FMM performance in accuracy and efficiency.

  13. Accurate, efficient, and scalable parallel simulation of mesoscale electrostatic/magnetostatic problems accelerated by a fast multipole method

    NASA Astrophysics Data System (ADS)

    Jiang, Xikai; Karpeev, Dmitry; Li, Jiyuan; de Pablo, Juan; Hernandez-Ortiz, Juan; Heinonen, Olle

    Boundary integrals arise in many electrostatic and magnetostatic problems. In computational modeling of these problems, although the integral is performed only on the boundary of a domain, its direct evaluation needs O(N2) operations, where N is number of unknowns on the boundary. The O(N2) scaling impedes a wider usage of the boundary integral method in scientific and engineering communities. We have developed a parallel computational approach that utilize the Fast Multipole Method to evaluate the boundary integral in O(N) operations. To demonstrate the accuracy, efficiency, and scalability of our approach, we consider two test cases. In the first case, we solve a boundary value problem for a ferroelectric/ferromagnetic volume in free space using a hybrid finite element-boundary integral method. In the second case, we solve an electrostatic problem involving the polarization of dielectric objects in free space using the boundary element method. The results from test cases show that our parallel approach can enable highly efficient and accurate simulations of mesoscale electrostatic/magnetostatic problems. Computing resources was provided by Blues, a high-performance cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory. Work at Argonne was supported by U. S. DOE, Office of Science under Contract No. DE-AC02-06CH11357.

  14. The fast multipole method and point dipole moment polarizable force fields

    NASA Astrophysics Data System (ADS)

    Coles, Jonathan P.; Masella, Michel

    2015-01-01

    We present an implementation of the fast multipole method for computing Coulombic electrostatic and polarization forces from polarizable force-fields based on induced point dipole moments. We demonstrate the expected O(N) scaling of that approach by performing single energy point calculations on hexamer protein subunits of the mature HIV-1 capsid. We also show the long time energy conservation in molecular dynamics at the nanosecond scale by performing simulations of a protein complex embedded in a coarse-grained solvent using a standard integrator and a multiple time step integrator. Our tests show the applicability of fast multipole method combined with state-of-the-art chemical models in molecular dynamical systems.

  15. The fast multipole method and point dipole moment polarizable force fields.

    PubMed

    Coles, Jonathan P; Masella, Michel

    2015-01-14

    We present an implementation of the fast multipole method for computing Coulombic electrostatic and polarization forces from polarizable force-fields based on induced point dipole moments. We demonstrate the expected O(N) scaling of that approach by performing single energy point calculations on hexamer protein subunits of the mature HIV-1 capsid. We also show the long time energy conservation in molecular dynamics at the nanosecond scale by performing simulations of a protein complex embedded in a coarse-grained solvent using a standard integrator and a multiple time step integrator. Our tests show the applicability of fast multipole method combined with state-of-the-art chemical models in molecular dynamical systems. PMID:25591340

  16. Comparing precorrected-FFT and fast multipole algorithms for solving three-dimensional potential integral equations

    SciTech Connect

    White, J.; Phillips, J.R.; Korsmeyer, T.

    1994-12-31

    Mixed first- and second-kind surface integral equations with (1/r) and {partial_derivative}/{partial_derivative} (1/r) kernels are generated by a variety of three-dimensional engineering problems. For such problems, Nystroem type algorithms can not be used directly, but an expansion for the unknown, rather than for the entire integrand, can be assumed and the product of the singular kernal and the unknown integrated analytically. Combining such an approach with a Galerkin or collocation scheme for computing the expansion coefficients is a general approach, but generates dense matrix problems. Recently developed fast algorithms for solving these dense matrix problems have been based on multipole-accelerated iterative methods, in which the fast multipole algorithm is used to rapidly compute the matrix-vector products in a Krylov-subspace based iterative method. Another approach to rapidly computing the dense matrix-vector products associated with discretized integral equations follows more along the lines of a multigrid algorithm, and involves projecting the surface unknowns onto a regular grid, then computing using the grid, and finally interpolating the results from the regular grid back to the surfaces. Here, the authors describe a precorrectted-FFT approach which can replace the fast multipole algorithm for accelerating the dense matrix-vector product associated with discretized potential integral equations. The precorrected-FFT method, described below, is an order n log(n) algorithm, and is asymptotically slower than the order n fast multipole algorithm. However, initial experimental results indicate the method may have a significant constant factor advantage for a variety of engineering problems.

  17. An efficient blocking M2L translation for low-frequency fast multipole method in three dimensions

    NASA Astrophysics Data System (ADS)

    Takahashi, Toru; Shimba, Yuta; Isakari, Hiroshi; Matsumoto, Toshiro

    2016-05-01

    We propose an efficient scheme to perform the multipole-to-local (M2L) translation in the three-dimensional low-frequency fast multipole method (LFFMM). Our strategy is to combine a group of matrix-vector products associated with M2L translation into a matrix-matrix product in order to diminish the memory traffic. For this purpose, we first developed a grouping method (termed as internal blocking) based on the congruent transformations (rotational and reflectional symmetries) of M2L-translators for each target box in the FMM hierarchy (adaptive octree). Next, we considered another method of grouping (termed as external blocking) that was able to handle M2L translations for multiple target boxes collectively by using the translational invariance of the M2L translation. By combining these internal and external blockings, the M2L translation can be performed efficiently whilst preservingthe numerical accuracy exactly. We assessed the proposed blocking scheme numerically and applied it to the boundary integral equation method to solve electromagnetic scattering problems for perfectly electrical conductor. From the numerical results, it was found that the proposed M2L scheme achieved a few times speedup compared to the non-blocking scheme.

  18. An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method

    NASA Astrophysics Data System (ADS)

    Zheng, Chang-Jun; Gao, Hai-Feng; Du, Lei; Chen, Hai-Bo; Zhang, Chuanzeng

    2016-01-01

    An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR (s) solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton-Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton-Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as α = i / k is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method.

  19. FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions

    NASA Astrophysics Data System (ADS)

    Huang, Jingfang; Jia, Jun; Zhang, Bo

    2009-11-01

    A Fortran program package is introduced for the rapid evaluation of the screened Coulomb interactions of N particles in three dimensions. The method utilizes an adaptive oct-tree structure, and is based on the new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related packages are also available at http://www.fastmultipole.org/. This paper is a brief review of the program and its performance. Catalogue identifier: AEEQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 12 385 No. of bytes in distributed program, including test data, etc.: 79 222 Distribution format: tar.gz Programming language: Fortran77 and Fortran90 Computer: Any Operating system: Any RAM: Depends on the number of particles, their distribution, and the adaptive tree structure Classification: 4.8, 4.12 Nature of problem: To evaluate the screened Coulomb potential and force field of N charged particles, and to evaluate a convolution type integral where the Green's function is the fundamental solution of the modified Helmholtz equation. Solution method: An adaptive oct-tree is generated, and a new version of fast multipole method is applied in which the "multipole-to-local" translation operator is diagonalized. Restrictions: Only three and six significant digits accuracy options are provided in this version. Unusual features: Most of the codes are written in

  20. Computing dislocation stress fields in anisotropic elastic media using fast multipole expansions

    NASA Astrophysics Data System (ADS)

    Yin, Jie; Barnett, D. M.; Fitzgerald, S. P.; Cai, Wei

    2012-06-01

    The calculation of stress fields due to dislocations and hence the forces they exert on each other is the most time consuming step in dislocation dynamics (DD) simulations. The fast multipole method (FMM) can reduce the computational cost at each simulation step from { O}(N^2) to { O}(N) for an ensemble of N dislocation segments. However, FMM has not yet been applied to three-dimensional DD simulations which take into account anisotropic elasticity. We demonstrate a systematic procedure to establish this capability by first obtaining the derivatives of the elastic Green's function to arbitrary order for a medium of general anisotropy. We then compute the stress field of a dislocation loop using multipole expansions based on these derivatives, and analyze the dependence of numerical errors on the expansion order. This method can be implemented in large scale DD simulations when the consideration of elastic anisotropy is necessary, for example the technologically important cases of iron and ferritic steels at high temperatures.

  1. Computation of scattering from clusters of spheres using the fast multipole method.

    PubMed

    Gumerov, Nail A; Duraiswami, Ramani

    2005-04-01

    A T-matrix based method of solution of the multiple scattering problem was presented by the authors [J. Acoust Soc. Am. 112, 2688-2701 (2002)]. This method can be applied to the computation of relatively small problems, since the number of operations required grows with the number of spheres N as O(N3), and with the sixth power of the wave number. The use of iterative techniques accelerated using the fast multipole method (FMM) can accelerate this solution, as presented by Koc and Chew [J. Acoust. Soc. Am. 103, 721-734 (1998)] originally. In this study we present a method that combines preconditioned Krylov subspace iterative techniques, FMM accelerated matrix vector products, a novel FMM-based preconditioner, and fast translation techniques that enable us to achieve an overall algorithm in which the cost of the matrix-vector multiplication grows with N as O (N logN) and with the third power of the wave number. We discuss the convergence of the iterative techniques, selection of the truncation number, errors in the solution, and other issues. The results of the solution of test problems obtained with the method for N approximately 10(2)-10(4) for different wave numbers are presented. PMID:15898622

  2. Computation of scattering from clusters of spheres using the fast multipole method

    NASA Astrophysics Data System (ADS)

    Gumerov, Nail A.; Duraiswami, Ramani

    2005-04-01

    A T-matrix based method of solution of the multiple scattering problem was presented by the authors [J. Acoust Soc. Am. 112, 2688-2701 (2002)]. This method can be applied to the computation of relatively small problems, since the number of operations required grows with the number of spheres N as O(N3), and with the sixth power of the wave number. The use of iterative techniques accelerated using the fast multipole method (FMM) can accelerate this solution, as presented by Koc and Chew [J. Acoust. Soc. Am. 103, 721-734 (1998)] originally. In this study we present a method that combines preconditioned Krylov subspace iterative techniques, FMM accelerated matrix vector products, a novel FMM-based preconditioner, and fast translation techniques that enable us to achieve an overall algorithm in which the cost of the matrix-vector multiplication grows with N as O(N log N) and with the third power of the wave number. We discuss the convergence of the iterative techniques, selection of the truncation number, errors in the solution, and other issues. The results of the solution of test problems obtained with the method for N~102-104 for different wave numbers are presented. .

  3. Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm.

    PubMed

    Ergül, Özgür; Gürel, Levent

    2013-03-01

    Accurate electromagnetic modeling of complicated optical structures poses several challenges. Optical metamaterial and plasmonic structures are composed of multiple coexisting dielectric and/or conducting parts. Such composite structures may possess diverse values of conductivities and dielectric constants, including negative permittivity and permeability. Further challenges are the large sizes of the structures with respect to wavelength and the complexities of the geometries. In order to overcome these challenges and to achieve rigorous and efficient electromagnetic modeling of three-dimensional optical composite structures, we have developed a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Precise formulation of composite structures is achieved with the so-called "electric and magnetic current combined-field integral equation." Surface integral equations are carefully discretized with piecewise linear basis functions, and the ensuing dense matrix equations are solved iteratively with parallel MLFMA. The hierarchical strategy is used for the efficient parallelization of MLFMA on distributed-memory architectures. In this paper, fast and accurate solutions of large-scale canonical and complicated real-life problems, such as optical metamaterials, discretized with tens of millions of unknowns are presented in order to demonstrate the capabilities of the proposed electromagnetic solver. PMID:23456127

  4. Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Schwörer, Magnus; Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

    2015-03-01

    Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 103-105 molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of the DFT and PMM-MD parts of the computation enables the efficient use of high-performance computing systems. The associated software is available online.

  5. Reduced-rank approximations to the far-field transform in the gridded fast multipole method

    NASA Astrophysics Data System (ADS)

    Hesford, Andrew J.; Waag, Robert C.

    2011-05-01

    The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.

  6. Fast Multipole Method for Coulomb Interaction Based on Traceless Totally Symmetric Tensor

    NASA Astrophysics Data System (ADS)

    Huang, He; Li, Rui; Chen, Jie; Luo, Li-Shi; Zhang, He

    2015-04-01

    The fast multipole method (FMM) is widely used to calculate the Coulomb interaction between a huge amount of charged particles. The efficiency of FMM scales with O(N) for N particles with any arbitrary distribution. Hence it is apposite for problems with complicated charge distribution or geometry. Under the same FMM framework, there are different approaches, such as using spherical harmonic functions or Maxwell Cartesian tensors. Here we will present a version using traceless totally symmetric Maxwell Cartesian tensor. The previous Maxwell Cartesian tensor based FMM uses totally symmetric tensor. There are (n + 1)(n + 2) / 2 independent elements in a rank n totally symmetric tensor. However, there are only 2 n + 1 independent elements in a rank n traceless totally symmetric tensor, due to which the efficiency of the traceless version is highly improved compared with the old version, especially when high accuracy is needed and high rank tensors are used. Work supported by the Department of Energy, Laboratory Directed Research and Development Funding, under Contract No. DE-AC05-06OR23177.

  7. Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations.

    PubMed

    Schwörer, Magnus; Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

    2015-03-14

    Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10(3)-10(5) molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of the DFT and PMM-MD parts of the computation enables the efficient use of high-performance computing systems. The associated software is available online. PMID:25770527

  8. Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations

    SciTech Connect

    Schwörer, Magnus; Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

    2015-03-14

    Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10{sup 3}-10{sup 5} molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of the DFT and PMM-MD parts of the computation enables the efficient use of high-performance computing systems. The associated software is available online.

  9. Preinflationary and inflationary fast-roll eras and their signatures in the low CMB multipoles

    NASA Astrophysics Data System (ADS)

    Destri, C.; de Vega, H. J.; Sanchez, N. G.

    2010-03-01

    =t*. The power spectrum gets dynamically modified by the effect of the fast-roll eras and the choice of Bunch-Davies initial conditions at a finite time through the transfer function D(k) of initial conditions. The power spectrum vanishes at k=0.D(k) presents a first peak for k˜2/η0 (η0 being the conformal initial time), then oscillates with decreasing amplitude and vanishes asymptotically for k→∞. The transfer function D(k) affects the low cosmic microwave background multipoles Cℓ: the change ΔCℓ/Cℓ for 1≤ℓ≤5 is computed as a function of the starting instant of the fluctuations t0. Cosmic microwave background quadrupole observations indicate large suppressions, which are well reproduced for the range t0-t*≳0.05/m≃10100tPlanck.

  10. Revision of FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions

    NASA Astrophysics Data System (ADS)

    Zhang, Bo; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai

    2010-12-01

    FMM-YUKAWA is a mathematical software package primarily for rapid evaluation of the screened Coulomb interactions of N particles in three dimensional space. Since its release, we have revised and re-organized the data structure, software architecture, and user interface, for the purpose of enabling more flexible, broader and easier use of the package. The package and its documentation are available at http://www.fastmultipole.org/, along with a few other closely related mathematical software packages. New version program summaryProgram title: FMM-Yukawa Catalogue identifier: AEEQ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEQ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 2.0 No. of lines in distributed program, including test data, etc.: 78 704 No. of bytes in distributed program, including test data, etc.: 854 265 Distribution format: tar.gz Programming language: FORTRAN 77, FORTRAN 90, and C. Requires gcc and gfortran version 4.4.3 or later Computer: All Operating system: Any Classification: 4.8, 4.12 Catalogue identifier of previous version: AEEQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2331 Does the new version supersede the previous version?: Yes Nature of problem: To evaluate the screened Coulomb potential and force field of N charged particles, and to evaluate a convolution type integral where the Green's function is the fundamental solution of the modified Helmholtz equation. Solution method: The new version of fast multipole method (FMM) that diagonalizes the multipole-to-local translation operator is applied with the tree structure adaptive to sample particle locations. Reasons for new version: To handle much larger particle ensembles, to enable the iterative use of the subroutines in a solver, and to remove potential contention in assignments for parallelization. Summary of revisions: The software package FMM-Yukawa has been

  11. Construction of wave-free potentials and multipoles in a two-layer fluid having free-surface boundary condition with higher-order derivatives

    NASA Astrophysics Data System (ADS)

    Das, Dilip

    2015-07-01

    There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace's equation (or Helmholtz equation) arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace's equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.

  12. The fast multipole method in the differential algebra framework for the calculation of 3D space charge fields

    NASA Astrophysics Data System (ADS)

    Zhang, He

    2013-01-01

    The space charge effect is one of the most important collective effects in beam dynamic studies. In many cases, numerical simulations are inevitable in order to get a clear understanding of this effect. The particle-particle interaction algorithms and the article-in-cell algorithms are widely used in space charge effect simulations. But they both have difficulties in dealing with highly correlated beams with abnormal distributions or complicated geometries. We developed a new algorithm to calculate the three dimensional self-field between charged particles by combining the differential algebra (DA) techniques with the fast multi-pole method (FMM). The FMM hierarchically decomposes the whole charged domain into many small regions. For each region it uses multipole expansions to represent the potential/field contributions from the particles far away from the region and then converts the multipole expansions into a local expansion inside the region. The potential/field due to the far away particles is calculated from the expansions and the potential/field due to the nearby particles is calculated from the Coulomb force law. The DA techniques are used in the calculation, translation and converting of the expansions. The new algorithm scales linearly with the total number of particles and it is suitable for any arbitrary charge distribution. Using the DA techniques, we can calculate both the potential/field and its high order derivatives, which will be useful for the purpose of including the space charge effect into transfer maps in the future. We first present the single level FMM, which decomposes the whole domain into boxes of the same size. It works best for charge distributions that are not overly non-uniform. Then we present the multilevel fast multipole algorithm (MLFMA), which decomposes the whole domain into different sized boxes according to the charge density. Finer boxes are generated where the higher charge density exists; thus the algorithm works for any

  13. Fast image restoration without boundary artifacts.

    PubMed

    Reeves, Stanley J

    2005-10-01

    Fast Fourier transform (FFT)-based restorations are fast, but at the expense of assuming that the blurring and deblurring are based on circular convolution. Unfortunately, when the opposite sides of the image do not match up well in intensity, this assumption can create significant artifacts across the image. If the pixels outside the measured image window are modeled as unknown values in the restored image, boundary artifacts are avoided. However, this approach destroys the structure that makes the use of the FFT directly applicable, since the unknown image is no longer the same size as the measured image. Thus, the restoration methods available for this problem no longer have the computational efficiency of the FFT. We propose a new restoration method for the unknown boundary approach that can be implemented in a fast and flexible manner. We decompose the restoration into a sum of two independent restorations. One restoration yields an image that comes directly from a modified FFT-based approach. The other restoration involves a set of unknowns whose number equals that of the unknown boundary values. By summing the two, the artifacts are canceled. Because the second restoration has a significantly reduced set of unknowns, it can be calculated very efficiently even though no circular convolution structure exists. PMID:16238051

  14. Combined fast multipole-QR compression technique for solving electrically small to large structures for broadband applications

    NASA Technical Reports Server (NTRS)

    Jandhyala, Vikram (Inventor); Chowdhury, Indranil (Inventor)

    2011-01-01

    An approach that efficiently solves for a desired parameter of a system or device that can include both electrically large fast multipole method (FMM) elements, and electrically small QR elements. The system or device is setup as an oct-tree structure that can include regions of both the FMM type and the QR type. An iterative solver is then used to determine a first matrix vector product for any electrically large elements, and a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large elements and the electrically small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter.

  15. An improved fast multipole method for electrostatic potential calculations in a class of coarse-grained molecular simulations

    SciTech Connect

    Poursina, Mohammad; Anderson, Kurt S.

    2014-08-01

    This paper presents a novel algorithm to approximate the long-range electrostatic potential field in the Cartesian coordinates applicable to 3D coarse-grained simulations of biopolymers. In such models, coarse-grained clusters are formed via treating groups of atoms as rigid and/or flexible bodies connected together via kinematic joints. Therefore, multibody dynamic techniques are used to form and solve the equations of motion of such coarse-grained systems. In this article, the approximations for the potential fields due to the interaction between a highly negatively/positively charged pseudo-atom and charged particles, as well as the interaction between clusters of charged particles, are presented. These approximations are expressed in terms of physical and geometrical properties of the bodies such as the entire charge, the location of the center of charge, and the pseudo-inertia tensor about the center of charge of the clusters. Further, a novel substructuring scheme is introduced to implement the presented far-field potential evaluations in a binary tree framework as opposed to the existing quadtree and octree strategies of implementing fast multipole method. Using the presented Lagrangian grids, the electrostatic potential is recursively calculated via sweeping two passes: assembly and disassembly. In the assembly pass, adjacent charged bodies are combined together to form new clusters. Then, the potential field of each cluster due to its interaction with faraway resulting clusters is recursively calculated in the disassembly pass. The method is highly compatible with multibody dynamic schemes to model coarse-grained biopolymers. Since the proposed method takes advantage of constant physical and geometrical properties of rigid clusters, improvement in the overall computational cost is observed comparing to the tradition application of fast multipole method.

  16. An O(N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

    NASA Astrophysics Data System (ADS)

    Jiang, Xikai; Li, Jiyuan; Zhao, Xujun; Qin, Jian; Karpeev, Dmitry; Hernandez-Ortiz, Juan; de Pablo, Juan J.; Heinonen, Olle

    2016-08-01

    Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct computational evaluation requires O(N2) operations, where N is the number of unknowns. Such a scaling, which arises from the many-body nature of the relevant Green's function, has precluded wide-spread adoption of integral methods for solution of large-scale scientific and engineering problems. In this work, a parallel computational approach is presented that relies on using scalable open source libraries and utilizes a kernel-independent Fast Multipole Method (FMM) to evaluate the integrals in O(N) operations, with O(N) memory cost, thereby substantially improving the scalability and efficiency of computational integral methods. We demonstrate the accuracy, efficiency, and scalability of our approach in the context of two examples. In the first, we solve a boundary value problem for a ferroelectric/ferromagnetic volume in free space. In the second, we solve an electrostatic problem involving polarizable dielectric bodies in an unbounded dielectric medium. The results from these test cases show that our proposed parallel approach, which is built on a kernel-independent FMM, can enable highly efficient and accurate simulations and allow for considerable flexibility in a broad range of applications.

  17. Fast Multipole Methods for Three-Dimensional N-body Problems

    NASA Technical Reports Server (NTRS)

    Koumoutsakos, P.

    1995-01-01

    We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995

  18. Multipole hydrophone

    SciTech Connect

    Cole, J.E. III

    1996-04-01

    Directional hydrophones provide the means to resolve bearing ambiguity in towed arrays and to reduce the effects of aliasing in undersampled arrays. A multipole hydrophone combines the output of multiple monopole elements spaced closely in terms of acoustic wavelengths to obtain its directionality. Issues related to multipole sensor implementation and performance include signal-to-noise performance, flow noise influence, and material selection. {copyright} {ital 1996 American Institute of Physics.}

  19. Computation of scattering matrix elements of large and complex shaped absorbing particles with multilevel fast multipole algorithm

    NASA Astrophysics Data System (ADS)

    Wu, Yueqian; Yang, Minglin; Sheng, Xinqing; Ren, Kuan Fang

    2015-05-01

    Light scattering properties of absorbing particles, such as the mineral dusts, attract a wide attention due to its importance in geophysical and environment researches. Due to the absorbing effect, light scattering properties of particles with absorption differ from those without absorption. Simple shaped absorbing particles such as spheres and spheroids have been well studied with different methods but little work on large complex shaped particles has been reported. In this paper, the surface Integral Equation (SIE) with Multilevel Fast Multipole Algorithm (MLFMA) is applied to study scattering properties of large non-spherical absorbing particles. SIEs are carefully discretized with piecewise linear basis functions on triangle patches to model whole surface of the particle, hence computation resource needs increase much more slowly with the particle size parameter than the volume discretized methods. To improve further its capability, MLFMA is well parallelized with Message Passing Interface (MPI) on distributed memory computer platform. Without loss of generality, we choose the computation of scattering matrix elements of absorbing dust particles as an example. The comparison of the scattering matrix elements computed by our method and the discrete dipole approximation method (DDA) for an ellipsoid dust particle shows that the precision of our method is very good. The scattering matrix elements of large ellipsoid dusts with different aspect ratios and size parameters are computed. To show the capability of the presented algorithm for complex shaped particles, scattering by asymmetry Chebyshev particle with size parameter larger than 600 of complex refractive index m = 1.555 + 0.004 i and different orientations are studied.

  20. The differential algebra based multiple level fast multipole algorithm for 3D space charge field calculation and photoemission simulation

    SciTech Connect

    None, None

    2015-09-28

    Coulomb interaction between charged particles inside a bunch is one of the most importance collective effects in beam dynamics, becoming even more significant as the energy of the particle beam is lowered to accommodate analytical and low-Z material imaging purposes such as in the time resolved Ultrafast Electron Microscope (UEM) development currently underway at Michigan State University. In addition, space charge effects are the key limiting factor in the development of ultrafast atomic resolution electron imaging and diffraction technologies and are also correlated with an irreversible growth in rms beam emittance due to fluctuating components of the nonlinear electron dynamics. In the short pulse regime used in the UEM, space charge effects also lead to virtual cathode formation in which the negative charge of the electrons emitted at earlier times, combined with the attractive surface field, hinders further emission of particles and causes a degradation of the pulse properties. Space charge and virtual cathode effects and their remediation are core issues for the development of the next generation of high-brightness UEMs. Since the analytical models are only applicable for special cases, numerical simulations, in addition to experiments, are usually necessary to accurately understand the space charge effect. In this paper we will introduce a grid-free differential algebra based multiple level fast multipole algorithm, which calculates the 3D space charge field for n charged particles in arbitrary distribution with an efficiency of O(n), and the implementation of the algorithm to a simulation code for space charge dominated photoemission processes.

  1. The differential algebra based multiple level fast multipole algorithm for 3D space charge field calculation and photoemission simulation

    DOE PAGESBeta

    None, None

    2015-09-28

    Coulomb interaction between charged particles inside a bunch is one of the most importance collective effects in beam dynamics, becoming even more significant as the energy of the particle beam is lowered to accommodate analytical and low-Z material imaging purposes such as in the time resolved Ultrafast Electron Microscope (UEM) development currently underway at Michigan State University. In addition, space charge effects are the key limiting factor in the development of ultrafast atomic resolution electron imaging and diffraction technologies and are also correlated with an irreversible growth in rms beam emittance due to fluctuating components of the nonlinear electron dynamics.more » In the short pulse regime used in the UEM, space charge effects also lead to virtual cathode formation in which the negative charge of the electrons emitted at earlier times, combined with the attractive surface field, hinders further emission of particles and causes a degradation of the pulse properties. Space charge and virtual cathode effects and their remediation are core issues for the development of the next generation of high-brightness UEMs. Since the analytical models are only applicable for special cases, numerical simulations, in addition to experiments, are usually necessary to accurately understand the space charge effect. In this paper we will introduce a grid-free differential algebra based multiple level fast multipole algorithm, which calculates the 3D space charge field for n charged particles in arbitrary distribution with an efficiency of O(n), and the implementation of the algorithm to a simulation code for space charge dominated photoemission processes.« less

  2. Accelerating Particle Filter Using Randomized Multiscale and Fast Multipole Type Methods.

    PubMed

    Shabat, Gil; Shmueli, Yaniv; Bermanis, Amit; Averbuch, Amir

    2015-07-01

    Particle filter is a powerful tool for state tracking using non-linear observations. We present a multiscale based method that accelerates the tracking computation by particle filters. Unlike the conventional way, which calculates weights over all particles in each cycle of the algorithm, we sample a small subset from the source particles using matrix decomposition methods. Then, we apply a function extension algorithm that uses a particle subset to recover the density function for all the rest of the particles not included in the chosen subset. The computational effort is substantial especially when multiple objects are tracked concurrently. The proposed algorithm significantly reduces the computational load. By using the Fast Gaussian Transform, the complexity of the particle selection step is reduced to a linear time in n and k, where n is the number of particles and k is the number of particles in the selected subset. We demonstrate our method on both simulated and on real data such as object tracking in video sequences. PMID:26352448

  3. Fast wave evanescence in filamentary boundary plasmas

    SciTech Connect

    Myra, J. R.

    2014-02-15

    Radio frequency waves for heating and current drive of plasmas in tokamaks and other magnetic confinement devices must first traverse the scrape-off-layer (SOL) before they can be put to their intended use. The SOL plasma is strongly turbulent and intermittent in space and time. These turbulent properties of the SOL, which are not routinely taken into account in wave propagation codes, can have an important effect on the coupling of waves through an evanescent SOL or edge plasma region. The effective scale length for fast wave (FW) evanescence in the presence of short-scale field-aligned filamentary plasma turbulence is addressed in this paper. It is shown that although the FW wavelength or evanescent scale length is long compared with the dimensions of the turbulence, the FW does not simply average over the turbulent density; rather, the average is over the exponentiation rate. Implications for practical situations are discussed.

  4. Multiple multipole program computation of periodic structures

    NASA Astrophysics Data System (ADS)

    Hafner, Ch.

    1995-05-01

    The three-dimensional multiple multipole program (MMP) code based on the generalized multipole technique is outlined for readers who are not familiar with its concepts. This code was originally designed for computational electromagnetics. Rayleigh expansions and periodic boundary conditions are two new features that make MMP computations of arbitrary periodic structures efficient and that at the same time allow us to take advantage of the benefits of other MMP features, including surface impedance boundary conditions and a variety of available basis functions for modeling the electromagnetic field. The application of three-dimensional MMP to a simple grating of highly conducting wires with rectangular cross sections illustrates the high accuracy and the fast convergence of the method as well as the use of surface impedance boundary conditions. A more complicated biperiodic array of helical antennas demonstrates the application of thin-wire expansions in conjunction with regular MMP expansions. This model can be considered a simulation of a thin, anisotropic chiral slab with interesting characteristics.

  5. Development of hardware accelerator for molecular dynamics simulations: a computation board that calculates nonbonded interactions in cooperation with fast multipole method.

    PubMed

    Amisaki, Takashi; Toyoda, Shinjiro; Miyagawa, Hiroh; Kitamura, Kunihiro

    2003-04-15

    Evaluation of long-range Coulombic interactions still represents a bottleneck in the molecular dynamics (MD) simulations of biological macromolecules. Despite the advent of sophisticated fast algorithms, such as the fast multipole method (FMM), accurate simulations still demand a great amount of computation time due to the accuracy/speed trade-off inherently involved in these algorithms. Unless higher order multipole expansions, which are extremely expensive to evaluate, are employed, a large amount of the execution time is still spent in directly calculating particle-particle interactions within the nearby region of each particle. To reduce this execution time for pair interactions, we developed a computation unit (board), called MD-Engine II, that calculates nonbonded pairwise interactions using a specially designed hardware. Four custom arithmetic-processors and a processor for memory manipulation ("particle processor") are mounted on the computation board. The arithmetic processors are responsible for calculation of the pair interactions. The particle processor plays a central role in realizing efficient cooperation with the FMM. The results of a series of 50-ps MD simulations of a protein-water system (50,764 atoms) indicated that a more stringent setting of accuracy in FMM computation, compared with those previously reported, was required for accurate simulations over long time periods. Such a level of accuracy was efficiently achieved using the cooperative calculations of the FMM and MD-Engine II. On an Alpha 21264 PC, the FMM computation at a moderate but tolerable level of accuracy was accelerated by a factor of 16.0 using three boards. At a high level of accuracy, the cooperative calculation achieved a 22.7-fold acceleration over the corresponding conventional FMM calculation. In the cooperative calculations of the FMM and MD-Engine II, it was possible to achieve more accurate computation at a comparable execution time by incorporating larger nearby

  6. Fast-sausage oscillations in coronal loops with smooth boundary

    NASA Astrophysics Data System (ADS)

    Lopin, I.; Nagorny, I.

    2014-12-01

    Aims: The effect of the transition layer (shell) in nonuniform coronal loops with a continuous radial density profile on the properties of fast-sausage modes are studied analytically and numerically. Methods: We modeled the coronal waveguide as a structured tube consisting of a cord and a transition region (shell) embedded within a magnetic uniform environment. The derived general dispersion relation was investigated analytically and numerically in the context of frequency, cut-off wave number, and the damping rate of fast-sausage oscillations for various values of loop parameters. Results: The frequency of the global fast-sausage mode in the loops with a diffuse (or smooth) boundary is determined mainly by the external Alfvén speed and longitudinal wave number. The damping rate of such a mode can be relatively low. The model of coronal loop with diffuse boundary can support a comparatively low-frequency, global fast-sausage mode of detectable quality without involving extremely low values of the density contrast. The effect of thin transition layer (corresponds to the loops with steep boundary) is negligible and produces small reductions of oscillation frequency and relative damping rate in comparison with the case of step-function density profile. Seismological application of obtained results gives the estimated Alfvén speed outside the flaring loop about 3.25 Mm/s.

  7. Gaussian Multipole Model (GMM)

    PubMed Central

    Elking, Dennis M.; Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.; Pedersen, Lee G.

    2009-01-01

    An electrostatic model based on charge density is proposed as a model for future force fields. The model is composed of a nucleus and a single Slater-type contracted Gaussian multipole charge density on each atom. The Gaussian multipoles are fit to the electrostatic potential (ESP) calculated at the B3LYP/6-31G* and HF/aug-cc-pVTZ levels of theory and tested by comparing electrostatic dimer energies, inter-molecular density overlap integrals, and permanent molecular multipole moments with their respective ab initio values. For the case of water, the atomic Gaussian multipole moments Qlm are shown to be a smooth function of internal geometry (bond length and bond angle), which can be approximated by a truncated linear Taylor series. In addition, results are given when the Gaussian multipole charge density is applied to a model for exchange-repulsion energy based on the inter-molecular density overlap. PMID:20209077

  8. Enhancement of the computational efficiency of the near-to-far field mapping in the finite-difference method and ray-by-ray method with the fast multi-pole plane wave expansion approach

    NASA Astrophysics Data System (ADS)

    Tang, Guanglin; Yang, Ping; Sun, Bingqiang; Panetta, R. Lee; Kattawar, George W.

    2016-06-01

    The finite-difference time-domain (FDTD) and ray-by-ray (RBR) methods are techniques used to calculate the optical properties of nonspherical particles for small-to-moderate and large size parameters, respectively. The former is a rigorous method, and the latter is an approximate geometric-physical optics-hybrid method that takes advantage of both high efficiency of the geometric optics approach and high accuracy of the physical optics approach. In these two methods, the far field is calculated by mapping the near field to the far field with consideration of the phase interference. The mapping computation is more time-consuming than the near-field simulation when multiple scattering directions are involved, particularly in the case of the RBR implementation. To overcome the difficulty, in this study the fast multi-pole method is applied to both FDTD and RBR towards accelerating the far-field calculation, without degrading the accuracy of the simulation results.

  9. Fast and accurate automated cell boundary determination for fluorescence microscopy

    NASA Astrophysics Data System (ADS)

    Arce, Stephen Hugo; Wu, Pei-Hsun; Tseng, Yiider

    2013-07-01

    Detailed measurement of cell phenotype information from digital fluorescence images has the potential to greatly advance biomedicine in various disciplines such as patient diagnostics or drug screening. Yet, the complexity of cell conformations presents a major barrier preventing effective determination of cell boundaries, and introduces measurement error that propagates throughout subsequent assessment of cellular parameters and statistical analysis. State-of-the-art image segmentation techniques that require user-interaction, prolonged computation time and specialized training cannot adequately provide the support for high content platforms, which often sacrifice resolution to foster the speedy collection of massive amounts of cellular data. This work introduces a strategy that allows us to rapidly obtain accurate cell boundaries from digital fluorescent images in an automated format. Hence, this new method has broad applicability to promote biotechnology.

  10. Direct determination of multipole moments of Cartesian Gaussian functions in spherical polar coordinates.

    PubMed

    Choi, Cheol Ho

    2004-02-22

    A new way of generating the multipole moments of Cartesian Gaussian functions in spherical polar coordinates has been established, bypassing the intermediary of Cartesian moment tensors. A new set of recurrence relations have also been derived for the resulting analytic integral values. The new method furnishes a conceptually simple and numerically efficient evaluation procedure for the multipole moments. The advantages over existing methods are documented. The results are relevant for the linear scaling quantum theories based on the fast multipole method. PMID:15268515

  11. Superconducting multipole corrector magnet

    SciTech Connect

    Kashikhin, Vladimir; /Fermilab

    2004-10-01

    A novel concept of superconducting multipole corrector magnet is discussed. This magnet assembled from 12 identical racetrack type coils and can generate any combination of dipole, quadrupole and sextupole magnetic fields. The coil groups are powered from separate power supplies. In the case of normal dipole, quadrupole and sextupole fields the total field is symmetrical relatively the magnet median plane and there are only five powered separately coil groups. This type multipole corrector magnet was proposed for BTeV, Fermilab project and has following advantages: universal configuration, simple manufacturing and high mechanical stability. The results of magnetic design including the field quality and magnetic forces in comparison with known shell type superconducting correctors are presented.

  12. AUTOMATIC GENERATION OF FFT FOR TRANSLATIONS OF MULTIPOLE EXPANSIONS IN SPHERICAL HARMONICS

    PubMed Central

    Mirkovic, Dragan; Pettitt, B. Montgomery; Johnsson, S. Lennart

    2009-01-01

    The fast multipole method (FMM) is an efficient algorithm for calculating electrostatic interactions in molecular simulations and a promising alternative to Ewald summation methods. Translation of multipole expansion in spherical harmonics is the most important operation of the fast multipole method and the fast Fourier transform (FFT) acceleration of this operation is among the fastest methods of improving its performance. The technique relies on highly optimized implementation of fast Fourier transform routines for the desired expansion sizes, which need to incorporate the knowledge of symmetries and zero elements in the input arrays. Here a method is presented for automatic generation of such, highly optimized, routines. PMID:19763233

  13. High beta multipoles

    SciTech Connect

    Prager, S C

    1982-05-01

    Multipoles are being employed as devices to study fusion issues and plasma phenomena at high values of beta (plasma pressure/magnetic pressure) in a controlled manner. Due to their large volume, low magnetic field (low synchrotron radiation) region, they are also under consideration as potential steady state advanced fuel (low neutron yield) reactors. Present experiments are investigating neoclassical (bootstrap and Pfirsch-Schlueter) currents and plasma stability at extremely high beta.

  14. Multipole plasmonic lattice solitons

    SciTech Connect

    Kou Yao; Ye Fangwei; Chen Xianfeng

    2011-09-15

    We theoretically demonstrate a variety of multipole plasmonic lattice solitons, including dipoles, quadrupoles, and necklaces, in two-dimensional metallic nanowire arrays with Kerr-type nonlinearities. Such solitons feature complex internal structures with an ultracompact mode size approaching or smaller than one wavelength. Their mode sizes and the stability characteristics are studied in detail within the framework of coupled mode theory. The conditions to form and stabilize these highly confined solitons are within the experimentally achievable range.

  15. HPAM: Hirshfeld Partitioned Atomic Multipoles

    PubMed Central

    Elking, Dennis M.; Perera, Lalith; Pedersen, Lee G.

    2011-01-01

    An implementation of the Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge density partitioning schemes is described. Atomic charges and atomic multipoles are calculated from the HD and HD-I atomic charge densities for arbitrary atomic multipole rank lmax on molecules of arbitrary shape and size. The HD and HD-I atomic charges/multipoles are tested by comparing molecular multipole moments and the electrostatic potential (ESP) surrounding a molecule with their reference ab initio values. In general, the HD-I atomic charges/multipoles are found to better reproduce ab initio electrostatic properties over HD atomic charges/multipoles. A systematic increase in precision for reproducing ab initio electrostatic properties is demonstrated by increasing the atomic multipole rank from lmax = 0 (atomic charges) to lmax = 4 (atomic hexadecapoles). Both HD and HD-I atomic multipoles up to rank lmax are shown to exactly reproduce ab initio molecular multipole moments of rank L for L ≤ lmax. In addition, molecular dipole moments calculated by HD, HD-I, and ChelpG atomic charges only (lmax = 0) are compared with reference ab initio values. Significant errors in reproducing ab initio molecular dipole moments are found if only HD or HD-I atomic charges used. PMID:22140274

  16. Monte Carlo simulations of electromagnetic wave scattering from a random rough surface with three-dimensional penetrable buried object: mine detection application using the steepest-descent fast multipole method.

    PubMed

    El-Shenawee, M; Rappaport, C; Silevitch, M

    2001-12-01

    We present a statistical study of the electric field scattered from a three-dimensional penetrable object buried under a two-dimensional random rough surface. Monte Carlo simulations using the steepest-descent fast multipole method (SDFMM) are conducted to calculate the average and the standard deviation of the near-zone scattered fields. The SDFMM, originally developed at the University of Illinois at Urbana-Champaign, has been modified to calculate the unknown surface currents both on the rough ground and on the buried object that are due to excitation by a tapered Gaussian beam. The rough ground medium used is an experimentally measured typical dry Bosnian soil with 3.8% moisture, while the buried object represents a plastic land mine modeled as an oblate spheroid with dimensions and burial depth smaller than the free-space wavelength. Both vertical and horizontal polarizations for the incident waves are studied. The numerical results show that the TNT mine signature is almost 5% of the total field scattered from the ground. Moreover, relatively recognizable object signatures are observed even when the object is buried under the tail of the incident beam. Interestingly, even for the small surface roughness parameters considered, the standard deviation of the object signature is almost 30% of the signal itself, indicating significant clutter distortion that is due to the roughness of the ground. PMID:11760205

  17. Directional spherical multipole wavelets

    SciTech Connect

    Hayn, Michael; Holschneider, Matthias

    2009-07-15

    We construct a family of admissible analysis reconstruction pairs of wavelet families on the sphere. The construction is an extension of the isotropic Poisson wavelets. Similar to those, the directional wavelets allow a finite expansion in terms of off-center multipoles. Unlike the isotropic case, the directional wavelets are not a tight frame. However, at small scales, they almost behave like a tight frame. We give an explicit formula for the pseudodifferential operator given by the combination analysis-synthesis with respect to these wavelets. The Euclidean limit is shown to exist and an explicit formula is given. This allows us to quantify the asymptotic angular resolution of the wavelets.

  18. Multipole Structure and Coordinate Systems

    ERIC Educational Resources Information Center

    Burko, Lior M.

    2007-01-01

    Multipole expansions depend on the coordinate system, so that coefficients of multipole moments can be set equal to zero by an appropriate choice of coordinates. Therefore, it is meaningless to say that a physical system has a nonvanishing quadrupole moment, say, without specifying which coordinate system is used. (Except if this moment is the…

  19. Interactive retinal vessel centreline extraction and boundary delineation using anisotropic fast marching and intensities consistency.

    PubMed

    Da Chen; Cohen, Laurent D

    2015-08-01

    In this paper, we propose a new interactive retinal vessels extraction method with anisotropic fast marching (AFM) based on the observation that one vessel may have the property of local intensities consistency. Our goal is to extract both the centrelines and boundaries between two given points. The proposed method consists of two stages: the first stage aims to finding the vessel centrelines using AFM and local intensities consistency roughly, while the second stage is to refine the centrelines from the previous stage using constrained Riemannian metric based AFM, and get the boundaries of the vessels simultaneously. Experiments show that results of our method outperform the classical minimal path method [1]. PMID:26737257

  20. Linear-scaling multipole-accelerated Gaussian and finite-element Coulomb method

    NASA Astrophysics Data System (ADS)

    Watson, Mark A.; Kurashige, Yuki; Nakajima, Takahito; Hirao, Kimihiko

    2008-02-01

    A linear-scaling implementation of the Gaussian and finite-element Coulomb (GFC) method is presented for the rapid computation of the electronic Coulomb potential. The current work utilizes the fast multipole method (FMM) for the evaluation of the Poisson equation boundary condition. The FMM affords significant savings for small- and medium-sized systems and overcomes the bottleneck in the GFC method for very large systems. Compared to an exact analytical treatment of the boundary, more than 100-fold speedups are observed for systems with more than 1000 basis functions without any significant loss of accuracy. We present CPU times to demonstrate the effectiveness of the linear-scaling GFC method for both one-dimensional polyalanine chains and the challenging case of three-dimensional diamond fragments.

  1. Melting of iron at Earth's inner core boundary based on fast X-ray diffraction.

    PubMed

    Anzellini, S; Dewaele, A; Mezouar, M; Loubeyre, P; Morard, G

    2013-04-26

    Earth's core is structured in a solid inner core, mainly composed of iron, and a liquid outer core. The temperature at the inner core boundary is expected to be close to the melting point of iron at 330 gigapascal (GPa). Despite intensive experimental and theoretical efforts, there is little consensus on the melting behavior of iron at these extreme pressures and temperatures. We present static laser-heated diamond anvil cell experiments up to 200 GPa using synchrotron-based fast x-ray diffraction as a primary melting diagnostic. When extrapolating to higher pressures, we conclude that the melting temperature of iron at the inner core boundary is 6230 ± 500 kelvin. This estimation favors a high heat flux at the core-mantle boundary with a possible partial melting of the mantle. PMID:23620049

  2. Orientation Measurement Based on Magnetic Inductance by the Extended Distributed Multi-Pole Model

    PubMed Central

    Wu, Fang; Moon, Seung Ki; Son, Hungsun

    2014-01-01

    This paper presents a novel method to calculate magnetic inductance with a fast-computing magnetic field model referred to as the extended distributed multi-pole (eDMP) model. The concept of mutual inductance has been widely applied for position/orientation tracking systems and applications, yet it is still challenging due to the high demands in robust modeling and efficient computation in real-time applications. Recently, numerical methods have been utilized in design and analysis of magnetic fields, but this often requires heavy computation and its accuracy relies on geometric modeling and meshing that limit its usage. On the other hand, an analytical method provides simple and fast-computing solutions but is also flawed due to its difficulties in handling realistic and complex geometries such as complicated designs and boundary conditions, etc. In this paper, the extended distributed multi-pole model (eDMP) is developed to characterize a time-varying magnetic field based on an existing DMP model analyzing static magnetic fields. The method has been further exploited to compute the mutual inductance between coils at arbitrary locations and orientations. Simulation and experimental results of various configurations of the coils are presented. Comparison with the previously published data shows not only good performance in accuracy, but also effectiveness in computation. PMID:24977389

  3. Fast photon-boundary intersection computation for Monte Carlo simulation of photon migration

    NASA Astrophysics Data System (ADS)

    Zhao, Xiaofen; Liu, Hongyan; Zhang, Bin; Liu, Fei; Luo, Jianwen; Bai, Jing

    2013-01-01

    Monte Carlo (MC) method is generally used as a "gold standard" technique to simulate photon transport in biomedical optics. However, it is quite time-consuming since abundant photon propagations need to be simulated in order to achieve an accurate result. In the case of complicated geometry, the computation speed is bound up with the calculation of the intersection between the photon transmission path and media boundary. The ray-triangle-based method is often used to calculate the photon-boundary intersection in the shape-based MC simulation for light propagation, but it is still relatively time-consuming. We present a fast way to determine the photon-boundary intersection. Triangle meshes are used to describe the boundary structure. A line segment instead of a ray is used to check if there exists a photon-boundary intersection, as the next location of the photon in light transports is determined by the step size. Results suggest that by simply replacing the conventional ray-triangle-based method with the proposed line segment-triangle-based method, the MC simulation for light propagation in the mouse model can be speeded up by more than 35%.

  4. Fast video shot boundary detection based on SVD and pattern matching.

    PubMed

    Lu, Zhe-Ming; Shi, Yong

    2013-12-01

    Video shot boundary detection (SBD) is the first and essential step for content-based video management and structural analysis. Great efforts have been paid to develop SBD algorithms for years. However, the high computational cost in the SBD becomes a block for further applications such as video indexing, browsing, retrieval, and representation. Motivated by the requirement of the real-time interactive applications, a unified fast SBD scheme is proposed in this paper. We adopted a candidate segment selection and singular value decomposition (SVD) to speed up the SBD. Initially, the positions of the shot boundaries and lengths of gradual transitions are predicted using adaptive thresholds and most non-boundary frames are discarded at the same time. Only the candidate segments that may contain the shot boundaries are preserved for further detection. Then, for all frames in each candidate segment, their color histograms in the hue-saturation-value) space are extracted, forming a frame-feature matrix. The SVD is then performed on the frame-feature matrices of all candidate segments to reduce the feature dimension. The refined feature vector of each frame in the candidate segments is obtained as a new metric for boundary detection. Finally, cut and gradual transitions are identified using our pattern matching method based on a new similarity measurement. Experiments on TRECVID 2001 test data and other video materials show that the proposed scheme can achieve a high detection speed and excellent accuracy compared with recent SBD schemes. PMID:24058028

  5. Multipole expansions and intense fields

    NASA Astrophysics Data System (ADS)

    Reiss, Howard R.

    1984-02-01

    In the context of two-body bound-state systems subjected to a plane-wave electromagnetic field, it is shown that high field intensity introduces a distinction between long-wavelength approximation and electric dipole approximation. This distinction is gauge dependent, since it is absent in Coulomb gauge, whereas in "completed" gauges of Göppert-Mayer type the presence of high field intensity makes electric quadrupole and magnetic dipole terms of importance equal to electric dipole at long wavelengths. Another consequence of high field intensity is that multipole expansions lose their utility in view of the equivalent importance of a number of low-order multipole terms and the appearance of large-magnitude terms which defy multipole categorization. This loss of the multipole expansion is gauge independent. Also gauge independent is another related consequence of high field intensity, which is the intimate coupling of center-of-mass and relative coordinate motions in a two-body system.

  6. Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems.

    PubMed

    Kowalczyk, P; Glendinning, P

    2011-06-01

    In this paper we study the qualitative dynamics of piecewise-smooth slow-fast systems (singularly perturbed systems) which are everywhere continuous. We consider phase space topology of systems with one-dimensional slow dynamics and one-dimensional fast dynamics. The slow manifold of the reduced system is formed by a piecewise-continuous curve, and the differentiability is lost across the switching surface. In the full system the slow manifold is no longer continuous, and there is an O(ɛ) discontinuity across the switching manifold, but the discontinuity cannot qualitatively alter system dynamics. Revealed phase space topology is used to unfold qualitative dynamics of planar slow-fast systems with an equilibrium point on the switching surface. In this case the local dynamics corresponds to so-called boundary-equilibrium bifurcations, and four qualitative phase portraits are uncovered. Our results are then used to investigate the dynamics of a box model of a thermohaline circulation, and the presence of a boundary-equilibrium bifurcation of a fold type is shown. PMID:21721768

  7. Fast finite difference methods for space-fractional diffusion equations with fractional derivative boundary conditions

    NASA Astrophysics Data System (ADS)

    Jia, Jinhong; Wang, Hong

    2015-07-01

    Numerical methods for space-fractional diffusion equations often generate dense or even full stiffness matrices. Traditionally, these methods were solved via Gaussian type direct solvers, which requires O (N3) of computational work per time step and O (N2) of memory to store where N is the number of spatial grid points in the discretization. In this paper we develop a preconditioned fast Krylov subspace iterative method for the efficient and faithful solution of finite difference methods (both steady-state and time-dependent) space-fractional diffusion equations with fractional derivative boundary conditions in one space dimension. The method requires O (N) of memory and O (Nlog ⁡ N) of operations per iteration. Due to the application of effective preconditioners, significantly reduced numbers of iterations were achieved that further reduces the computational cost of the fast method. Numerical results are presented to show the utility of the method.

  8. Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding

    PubMed Central

    Kreienkamp, Amelia B.; Liu, Lucy Y.; Minkara, Mona S.; Knepley, Matthew G.; Bardhan, Jaydeep P.; Radhakrishnan, Mala L.

    2013-01-01

    We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins—a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein–protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models’ differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundary-integral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes. PMID:24466561

  9. Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding.

    PubMed

    Kreienkamp, Amelia B; Liu, Lucy Y; Minkara, Mona S; Knepley, Matthew G; Bardhan, Jaydeep P; Radhakrishnan, Mala L

    2013-06-01

    We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins-a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein-protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models' differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundary-integral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes. PMID:24466561

  10. A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

    NASA Technical Reports Server (NTRS)

    Hu, Fang Q.

    1994-01-01

    It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

  11. Boundary identification in EBSD data with a generalization of fast multiscale clustering.

    PubMed

    McMahon, Cullen; Soe, Brian; Loeb, Andrew; Vemulkar, Ayyappa; Ferry, Michael; Bassman, Lori

    2013-10-01

    Electron backscatter diffraction (EBSD) studies of cellular or subgrain microstructures present problems beyond those in the study of coarse-grained polycrystalline aggregates. In particular, identification of boundaries delineating some subgrain structures, such as microbands, cannot be accomplished simply with pixel-to-pixel misorientation thresholding because many of the boundaries are gradual transitions in crystallographic orientation. Fast multiscale clustering (FMC) is an established data segmentation technique that is combined here with quaternion representation of orientation to segment EBSD data with gradual transitions. This implementation of FMC addresses a common problem with segmentation algorithms, handling data sets with both high and low magnitude boundaries, by using a novel distance function that is a modification of Mahalanobis distance. It accommodates data representations, such as quaternions, whose features are not necessarily linearly correlated but have known distance functions. To maintain the linear run time of FMC with such data, the method requires a novel variance update rule. Although FMC was originally an algorithm for two-dimensional data segmentation, it can be generalized to analyze three-dimensional data sets. As examples, several segmentations of quaternion EBSD data sets are presented. PMID:23751208

  12. Superconductivity in magnetic multipole states

    NASA Astrophysics Data System (ADS)

    Sumita, Shuntaro; Yanase, Youichi

    2016-06-01

    Stimulated by recent studies of superconductivity and magnetism with local and global broken inversion symmetry, we investigate the superconductivity in magnetic multipole states in locally noncentrosymmetric metals. We consider a one-dimensional zigzag chain with sublattice-dependent antisymmetric spin-orbit coupling and suppose three magnetic multipole orders: monopole order, dipole order, and quadrupole order. It is demonstrated that the Bardeen-Cooper-Schrieffer state, the pair-density wave (PDW) state, and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are stabilized by these multipole orders, respectively. We show that the PDW state is a topological superconducting state specified by the nontrivial Z2 number and winding number. The origin of the FFLO state without macroscopic magnetic moment is attributed to the asymmetric band structure induced by the magnetic quadrupole order and spin-orbit coupling.

  13. Radiation reaction of multipole moments

    NASA Astrophysics Data System (ADS)

    Kazinski, P. O.

    2007-08-01

    A Poincaré-invariant description is proposed for the effective dynamics of a localized system of charged particles in classical electrodynamics in terms of the intrinsic multipole moments of the system. A relativistic-invariant definition for the intrinsic multipole moments of a system of charged particles is given. A new generally covariant action functional for a relativistic perfect fluid is proposed. In the case of relativistic charged dust, it is proven that the description of the problem of radiation reaction of multipole moments by the model of particles is equivalent to the description of this problem by a hydrodynamic model. An effective model is obtained for a pointlike neutral system of charged particles that possesses an intrinsic dipole moment, and the free dynamics of this system is described. The bound momentum of a point dipole is found.

  14. CATHEDRAL: A Fast and Effective Algorithm to Predict Folds and Domain Boundaries from Multidomain Protein Structures

    PubMed Central

    Dallman, Tim; Pearl, Frances M. G; Orengo, Christine A

    2007-01-01

    We present CATHEDRAL, an iterative protocol for determining the location of previously observed protein folds in novel multidomain protein structures. CATHEDRAL builds on the features of a fast secondary-structure–based method (using graph theory) to locate known folds within a multidomain context and a residue-based, double-dynamic programming algorithm, which is used to align members of the target fold groups against the query protein structure to identify the closest relative and assign domain boundaries. To increase the fidelity of the assignments, a support vector machine is used to provide an optimal scoring scheme. Once a domain is verified, it is excised, and the search protocol is repeated in an iterative fashion until all recognisable domains have been identified. We have performed an initial benchmark of CATHEDRAL against other publicly available structure comparison methods using a consensus dataset of domains derived from the CATH and SCOP domain classifications. CATHEDRAL shows superior performance in fold recognition and alignment accuracy when compared with many equivalent methods. If a novel multidomain structure contains a known fold, CATHEDRAL will locate it in 90% of cases, with <1% false positives. For nearly 80% of assigned domains in a manually validated test set, the boundaries were correctly delineated within a tolerance of ten residues. For the remaining cases, previously classified domains were very remotely related to the query chain so that embellishments to the core of the fold caused significant differences in domain sizes and manual refinement of the boundaries was necessary. To put this performance in context, a well-established sequence method based on hidden Markov models was only able to detect 65% of domains, with 33% of the subsequent boundaries assigned within ten residues. Since, on average, 50% of newly determined protein structures contain more than one domain unit, and typically 90% or more of these domains are already

  15. Development of Fast Algorithms Using Recursion, Nesting and Iterations for Computational Electromagnetics

    NASA Technical Reports Server (NTRS)

    Chew, W. C.; Song, J. M.; Lu, C. C.; Weedon, W. H.

    1995-01-01

    In the first phase of our work, we have concentrated on laying the foundation to develop fast algorithms, including the use of recursive structure like the recursive aggregate interaction matrix algorithm (RAIMA), the nested equivalence principle algorithm (NEPAL), the ray-propagation fast multipole algorithm (RPFMA), and the multi-level fast multipole algorithm (MLFMA). We have also investigated the use of curvilinear patches to build a basic method of moments code where these acceleration techniques can be used later. In the second phase, which is mainly reported on here, we have concentrated on implementing three-dimensional NEPAL on a massively parallel machine, the Connection Machine CM-5, and have been able to obtain some 3D scattering results. In order to understand the parallelization of codes on the Connection Machine, we have also studied the parallelization of 3D finite-difference time-domain (FDTD) code with PML material absorbing boundary condition (ABC). We found that simple algorithms like the FDTD with material ABC can be parallelized very well allowing us to solve within a minute a problem of over a million nodes. In addition, we have studied the use of the fast multipole method and the ray-propagation fast multipole algorithm to expedite matrix-vector multiplication in a conjugate-gradient solution to integral equations of scattering. We find that these methods are faster than LU decomposition for one incident angle, but are slower than LU decomposition when many incident angles are needed as in the monostatic RCS calculations.

  16. Multipole expansion method for supernova neutrino oscillations

    SciTech Connect

    Duan, Huaiyu; Shalgar, Shashank E-mail: shashankshalgar@unm.edu

    2014-10-01

    We demonstrate a multipole expansion method to calculate collective neutrino oscillations in supernovae using the neutrino bulb model. We show that it is much more efficient to solve multi-angle neutrino oscillations in multipole basis than in angle basis. The multipole expansion method also provides interesting insights into multi-angle calculations that were accomplished previously in angle basis.

  17. Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform.

    PubMed

    Zuo, Chao; Chen, Qian; Asundi, Anand

    2014-04-21

    The transport of intensity equation (TIE) is a two-dimensional second order elliptic partial differential equation that must be solved under appropriate boundary conditions. However, the boundary conditions are difficult to obtain in practice. The fast Fourier transform (FFT) based TIE solutions are widely adopted for its speed and simplicity. However, it implies periodic boundary conditions, which lead to significant boundary artifacts when the imposed assumption is violated. In this work, TIE phase retrieval is considered as an inhomogeneous Neumann boundary value problem with the boundary values experimentally measurable around a hard-edged aperture, without any assumption or prior knowledge about the test object and the setup. The analytic integral solution via Green's function is given, as well as a fast numerical implementation for a rectangular region using the discrete cosine transform. This approach is applicable for the case of non-uniform intensity distribution with no extra effort to extract the boundary values from the intensity derivative signals. Its efficiency and robustness have been verified by several numerical simulations even when the objects are complex and the intensity measurements are noisy. This method promises to be an effective fast TIE solver for quantitative phase imaging applications. PMID:24787811

  18. Receptivity of hypersonic boundary layer due to fast-slow acoustics interaction

    NASA Astrophysics Data System (ADS)

    Gao, Jun; Luo, Ji-Sheng; Wu, Xue-Song

    2015-12-01

    The objective of receptivity is to investigate the mechanisms by which external disturbances generate unstable waves. In hypersonic boundary layers, a new receptivity process is revealed, which is that fast and slow acoustics through nonlinear interaction can excite the second mode near the lower-branch of the second mode. They can generate a sum-frequency disturbance though nonlinear interaction, which can excite the second mode. This receptivity process is generated by the nonlinear interaction and the nonparallel nature of the boundary layer. The receptivity coefficient is sensitive to the wavenumber difference between the sum-frequency disturbance and the lower-branch second mode. When the wavenumber difference is zero, the receptivity coefficient is maximum. The receptivity coefficient decreases with the increase of the wavenumber difference. It is also found that the evolution of the sum-frequency disturbance grows linearly in the beginning. It indicates that the forced term generated by the sum-frequency disturbance resonates with the second mode.

  19. A fast boundary element method for the scattering analysis of high-intensity focused ultrasound.

    PubMed

    van 't Wout, Elwin; Gélat, Pierre; Betcke, Timo; Arridge, Simon

    2015-11-01

    High-intensity focused ultrasound (HIFU) techniques are promising modalities for the non-invasive treatment of cancer. For HIFU therapies of, e.g., liver cancer, one of the main challenges is the accurate focusing of the acoustic field inside a ribcage. Computational methods can play an important role in the patient-specific planning of these transcostal HIFU treatments. This requires the accurate modeling of acoustic scattering at ribcages. The use of a boundary element method (BEM) is an effective approach for this purpose because only the boundaries of the ribs have to be discretized instead of the standard approach to model the entire volume around the ribcage. This paper combines fast algorithms that improve the efficiency of BEM specifically for the high-frequency range necessary for transcostal HIFU applications. That is, a Galerkin discretized Burton-Miller formulation is used in combination with preconditioning and matrix compression techniques. In particular, quick convergence is achieved with the operator preconditioner that has been designed with on-surface radiation conditions for the high-frequency approximation of the Neumann-to-Dirichlet map. Realistic computations of acoustic scattering at 1 MHz on a human ribcage model demonstrate the effectiveness of this dedicated BEM algorithm for HIFU scattering analysis. PMID:26627749

  20. The Relationship of Ion Beams and Fast Flows in the Plasma Sheet Boundary Layer

    NASA Technical Reports Server (NTRS)

    Parks, G. K.; Reme, H.; Lin, R. P.; Sanderson, T.; Germany, G. A.; Spann, James F., Jr.; Brittnacher, M. J.; McCarthy, M.; Chen, L. J.; Larsen, D.; Phan, T. D.

    1998-01-01

    We report new findings on the behavior of plasmas in the vicinity of the plasma sheet boundary layer (PSBL). A large geometrical factor detector on WIND (3D plasma experiment) has discovered a unidirectional ion beam streaming in the tailward direction missed by previous observations. This tailward beam is as intense as the earthward streaming beam and it is found just inside the outer edge of the PSBL where earthward streaming beams are observed. The region where this tailward beam is observed includes an isotropic plasma component which is absent in the outer edge where earthward streaming beams are found. When these different distributions are convolved to calculate the velocity moments, fast flows (greater than 400 km/s) result in the earthward direction and much slower flows (less than 200 km/s) in the tailward direction. These new findings are substantially different from previous observations. Thus, the interpretation of fast flows and earthward and counterstreaming ion beams in terms of a neutral line model must be reexamined.

  1. A Fast Poisson Solver with Periodic Boundary Conditions for GPU Clusters in Various Configurations

    NASA Astrophysics Data System (ADS)

    Rattermann, Dale Nicholas

    Fast Poisson solvers using the Fast Fourier Transform on uniform grids are especially suited for parallel implementation, making them appropriate for portability on graphical processing unit (GPU) devices. The goal of the following work was to implement, test, and evaluate a fast Poisson solver for periodic boundary conditions for use on a variety of GPU configurations. The solver used in this research was FLASH, an immersed-boundary-based method, which is well suited for complex, time-dependent geometries, has robust adaptive mesh refinement/de-refinement capabilities to capture evolving flow structures, and has been successfully implemented on conventional, parallel supercomputers. However, these solvers are still computationally costly to employ, and the total solver time is dominated by the solution of the pressure Poisson equation using state-of-the-art multigrid methods. FLASH improves the performance of its multigrid solvers by integrating a parallel FFT solver on a uniform grid during a coarse level. This hybrid solver could then be theoretically improved by replacing the highly-parallelizable FFT solver with one that utilizes GPUs, and, thus, was the motivation for my research. In the present work, the CPU-utilizing parallel FFT solver (PFFT) used in the base version of FLASH for solving the Poisson equation on uniform grids has been modified to enable parallel execution on CUDA-enabled GPU devices. New algorithms have been implemented to replace the Poisson solver that decompose the computational domain and send each new block to a GPU for parallel computation. One-dimensional (1-D) decomposition of the computational domain minimizes the amount of network traffic involved in this bandwidth-intensive computation by limiting the amount of all-to-all communication required between processes. Advanced techniques have been incorporated and implemented in a GPU-centric code design, while allowing end users the flexibility of parameter control at runtime in

  2. An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

    NASA Technical Reports Server (NTRS)

    Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

    1986-01-01

    A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

  3. Polarizable atomic multipole X-ray refinement: application to peptide crystals

    SciTech Connect

    Schnieders, Michael J.; Fenn, Timothy D.; Pande, Vijay S.; Brunger, Axel T.

    2009-09-01

    A method to accelerate the computation of structure factors from an electron density described by anisotropic and aspherical atomic form factors via fast Fourier transformation is described for the first time. Recent advances in computational chemistry have produced force fields based on a polarizable atomic multipole description of biomolecular electrostatics. In this work, the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field is applied to restrained refinement of molecular models against X-ray diffraction data from peptide crystals. A new formalism is also developed to compute anisotropic and aspherical structure factors using fast Fourier transformation (FFT) of Cartesian Gaussian multipoles. Relative to direct summation, the FFT approach can give a speedup of more than an order of magnitude for aspherical refinement of ultrahigh-resolution data sets. Use of a sublattice formalism makes the method highly parallelizable. Application of the Cartesian Gaussian multipole scattering model to a series of four peptide crystals using multipole coefficients from the AMOEBA force field demonstrates that AMOEBA systematically underestimates electron density at bond centers. For the trigonal and tetrahedral bonding geometries common in organic chemistry, an atomic multipole expansion through hexadecapole order is required to explain bond electron density. Alternatively, the addition of interatomic scattering (IAS) sites to the AMOEBA-based density captured bonding effects with fewer parameters. For a series of four peptide crystals, the AMOEBA–IAS model lowered R{sub free} by 20–40% relative to the original spherically symmetric scattering model.

  4. Hybrid Finite Element-Fast Spectral Domain Multilayer Boundary Integral Modeling of Doubly Periodic Structures

    SciTech Connect

    T.F. Eibert; J.L. Volakis; Y.E. Erdemli

    2002-03-03

    Hybrid finite element (FE)--boundary integral (BI) analysis of infinite periodic arrays is extended to include planar multilayered Green's functions. In this manner, a portion of the volumetric dielectric region can be modeled via the finite element method whereas uniform multilayered regions can be modeled using a multilayered Green's function. As such, thick uniform substrates can be modeled without loss of efficiency and accuracy. The multilayered Green's function is analytically computed in the spectral domain and the resulting BI matrix-vector products are evaluated via the fast spectral domain algorithm (FSDA). As a result, the computational cost of the matrix-vector products is kept at O(N). Furthermore, the number of Floquet modes in the expansion are kept very few by placing the BI surfaces within the computational unit cell. Examples of frequency selective surface (FSS) arrays are analyzed with this method to demonstrate the accuracy and capability of the approach. One example involves complicated multilayered substrates above and below an inhomogeneous filter element and the other is an optical ring-slot array on a substrate several hundred wavelengths in thickness. Comparisons with measurements are included.

  5. Molecular Multipole Potential Energy Functions for Water.

    PubMed

    Tan, Ming-Liang; Tran, Kelly N; Pickard, Frank C; Simmonett, Andrew C; Brooks, Bernard R; Ichiye, Toshiko

    2016-03-01

    Water is the most common liquid on this planet, with many unique properties that make it essential for life as we know it. These properties must arise from features in the charge distribution of a water molecule, so it is essential to capture these features in potential energy functions for water to reproduce its liquid state properties in computer simulations. Recently, models that utilize a multipole expansion located on a single site in the water molecule, or "molecular multipole models", have been shown to rival and even surpass site models with up to five sites in reproducing both the electrostatic potential around a molecule and a variety of liquid state properties in simulations. However, despite decades of work using multipoles, confusion still remains about how to truncate the multipole expansions efficiently and accurately. This is particularly important when using molecular multipole expansions to describe water molecules in the liquid state, where the short-range interactions must be accurate, because the higher order multipoles of a water molecule are large. Here, truncation schemes designed for a recent efficient algorithm for multipoles in molecular dynamics simulations are assessed for how well they reproduce results for a simple three-site model of water when the multipole moments and Lennard-Jones parameters of that model are used. In addition, the multipole analysis indicates that site models that do not account for out-of-plane electron density overestimate the stability of a non-hydrogen-bonded conformation, leading to serious consequences for the simulated liquid. PMID:26562223

  6. Comparison of scalable fast methods for long-range interactions.

    PubMed

    Arnold, Axel; Fahrenberger, Florian; Holm, Christian; Lenz, Olaf; Bolten, Matthias; Dachsel, Holger; Halver, Rene; Kabadshow, Ivo; Gähler, Franz; Heber, Frederik; Iseringhausen, Julian; Hofmann, Michael; Pippig, Michael; Potts, Daniel; Sutmann, Godehard

    2013-12-01

    Based on a parallel scalable library for Coulomb interactions in particle systems, a comparison between the fast multipole method (FMM), multigrid-based methods, fast Fourier transform (FFT)-based methods, and a Maxwell solver is provided for the case of three-dimensional periodic boundary conditions. These methods are directly compared with respect to complexity, scalability, performance, and accuracy. To ensure comparable conditions for all methods and to cover typical applications, we tested all methods on the same set of computers using identical benchmark systems. Our findings suggest that, depending on system size and desired accuracy, the FMM- and FFT-based methods are most efficient in performance and stability. PMID:24483585

  7. Polarizable atomic multipole X-ray refinement: application to peptide crystals

    PubMed Central

    Schnieders, Michael J.; Fenn, Timothy D.; Pande, Vijay S.; Brunger, Axel T.

    2009-01-01

    Recent advances in computational chemistry have produced force fields based on a polarizable atomic multipole description of biomolecular electrostatics. In this work, the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field is applied to restrained refinement of molecular models against X-ray diffraction data from peptide crystals. A new formalism is also developed to compute anisotropic and aspherical structure factors using fast Fourier transformation (FFT) of Cartesian Gaussian multipoles. Relative to direct summation, the FFT approach can give a speedup of more than an order of magnitude for aspherical refinement of ultrahigh-resolution data sets. Use of a sublattice formalism makes the method highly parallelizable. Application of the Cartesian Gaussian multipole scattering model to a series of four peptide crystals using multipole coefficients from the AMOEBA force field demonstrates that AMOEBA systematically underestimates electron density at bond centers. For the trigonal and tetrahedral bonding geometries common in organic chemistry, an atomic multipole expansion through hexadecapole order is required to explain bond electron density. Alternatively, the addition of inter­atomic scattering (IAS) sites to the AMOEBA-based density captured bonding effects with fewer parameters. For a series of four peptide crystals, the AMOEBA–IAS model lowered R free by 20–40% relative to the original spherically symmetric scattering model. PMID:19690373

  8. Smooth Teeth: Why Multipoles Are Perfect Gears

    NASA Astrophysics Data System (ADS)

    Schönke, Johannes

    2015-12-01

    A type of gear is proposed based on the interaction of individual multipoles. The underlying principle relies on previously unknown continuous degenerate ground states for pairs of interacting multipoles which are free to rotate around specific axes. These special rotation axes, in turn, form a one-parameter family of possible configurations. This allows for the construction of magnetic bevel gears with any desired inclination angle between the in- and output axes. Further, the design of gear systems with more than two multipoles is possible and facilitates tailored applications. Ultimately, an analogy between multipoles and mechanical gears is revealed. In contrast to the mechanical case, the multipole "teeth" mesh smoothly. As an illustrative application, the example of a quadrupole-dipole interaction is then used to construct a 1 ∶2 gear ratio.

  9. A single-site multipole model for liquid water

    NASA Astrophysics Data System (ADS)

    Tran, Kelly N.; Tan, Ming-Liang; Ichiye, Toshiko

    2016-07-01

    Accurate and efficient empirical potential energy models that describe the atomistic interactions between water molecules in the liquid phase are essential for computer simulations of many problems in physics, chemistry, and biology, especially when long length or time scales are important. However, while models with non-polarizable partial charges at four or five sites in a water molecule give remarkably good values for certain properties, deficiencies have been noted in other properties and increasing the number of sites decreases computational efficiency. An alternate approach is to utilize a multipole expansion of the electrostatic potential due to the molecular charge distribution, which is exact outside the charge distribution in the limits of infinite distances or infinite orders of multipoles while partial charges are a qualitative representation of electron density as point charges. Here, a single-site multipole model of water is presented, which is as fast computationally as three-site models but is also more accurate than four- and five-site models. The dipole, quadrupole, and octupole moments are from quantum mechanical-molecular mechanical calculations so that they account for the average polarization in the liquid phase, and represent both the in-plane and out-of-plane electrostatic potentials of a water molecule in the liquid phase. This model gives accurate thermodynamic, dynamic, and dielectric properties at 298 K and 1 atm, as well as good temperature and pressure dependence of these properties.

  10. A single-site multipole model for liquid water.

    PubMed

    Tran, Kelly N; Tan, Ming-Liang; Ichiye, Toshiko

    2016-07-21

    Accurate and efficient empirical potential energy models that describe the atomistic interactions between water molecules in the liquid phase are essential for computer simulations of many problems in physics, chemistry, and biology, especially when long length or time scales are important. However, while models with non-polarizable partial charges at four or five sites in a water molecule give remarkably good values for certain properties, deficiencies have been noted in other properties and increasing the number of sites decreases computational efficiency. An alternate approach is to utilize a multipole expansion of the electrostatic potential due to the molecular charge distribution, which is exact outside the charge distribution in the limits of infinite distances or infinite orders of multipoles while partial charges are a qualitative representation of electron density as point charges. Here, a single-site multipole model of water is presented, which is as fast computationally as three-site models but is also more accurate than four- and five-site models. The dipole, quadrupole, and octupole moments are from quantum mechanical-molecular mechanical calculations so that they account for the average polarization in the liquid phase, and represent both the in-plane and out-of-plane electrostatic potentials of a water molecule in the liquid phase. This model gives accurate thermodynamic, dynamic, and dielectric properties at 298 K and 1 atm, as well as good temperature and pressure dependence of these properties. PMID:27448890

  11. Windowed multipole for cross section Doppler broadening

    NASA Astrophysics Data System (ADS)

    Josey, C.; Ducru, P.; Forget, B.; Smith, K.

    2016-02-01

    This paper presents an in-depth analysis on the accuracy and performance of the windowed multipole Doppler broadening method. The basic theory behind cross section data is described, along with the basic multipole formalism followed by the approximations leading to windowed multipole method and the algorithm used to efficiently evaluate Doppler broadened cross sections. The method is tested by simulating the BEAVRS benchmark with a windowed multipole library composed of 70 nuclides. Accuracy of the method is demonstrated on a single assembly case where total neutron production rates and 238U capture rates compare within 0.1% to ACE format files at the same temperature. With regards to performance, clock cycle counts and cache misses were measured for single temperature ACE table lookup and for windowed multipole. The windowed multipole method was found to require 39.6% more clock cycles to evaluate, translating to a 7.9% performance loss overall. However, the algorithm has significantly better last-level cache performance, with 3 fewer misses per evaluation, or a 65% reduction in last-level misses. This is due to the small memory footprint of the windowed multipole method and better memory access pattern of the algorithm.

  12. The elliptical multipole wiggler project

    SciTech Connect

    Gluskin, E.; Frachon, D.; Ivanov, P.M.

    1995-06-01

    The elliptical multipole wiggler (EMW) has been designed, constructed, and installed in the X13 straight section of the NSLS X-ray Ring. The EMW generates circularly polarized photons in the energy range of 0.1-10 keV with AC modulation of polarization helicity. The vertical magnetic field of 0.8 T is produced by a hybrid permanent magnet structure with a period of 16 cm. The horizontal magnetic field of 0.22 T is generated by an electromagnet, the core of which is fabricated from laminated iron to operate with a switching frequency up to 100 Hz. There are dynamic compensation trim magnets at the wiggler ends to control the first and second field integrals with very high accuracy throughout the AC cycle. The residual closed orbit motion due to the electromagnet AC operation is discussed.

  13. 15 cm multipole gas ion thruster

    NASA Technical Reports Server (NTRS)

    Isaacson, G. C.; Kaufman, H. R.

    1976-01-01

    A 15-cm multipole thruster was operated on argon and xenon. The multipole approach used has been shown capable of low discharge losses and flat ion beam profiles with a minimum of redesign. This approach employs low magnetic field strengths and flat or cylindrical sheet-metal parts, hence is suited to rapid optimization and scaling. Only refractory metal cathodes were used in this investigation.

  14. Wavelet multiresolution analyses adapted for the fast solution of boundary value ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Jawerth, Bjoern; Sweldens, Wim

    1993-01-01

    We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators.

  15. Suppressing CMB low multipoles with ISW effect

    SciTech Connect

    Das, Santanu; Souradeep, Tarun E-mail: tarun@iucaa.ernet.in

    2014-02-01

    Recent results of Planck data reveal that the power [1,2] in the low multipoles of the CMB angular power spectrum, approximately up to l = 30, is significantly lower than the theoretically predicted in the best fit ΛCDM model. There are different known physical effects that can affect the power at low multipoles, such as features in the primordial power spectrum (PPS) in some models of inflation and ISW effect. In this paper we investigate the possibility of invoking the Integrated Sachs-Wolfe (ISW) effect to explain the power deficit at low multipoles. The ISW effect that originates from the late time expansion history of the universe is rich in possibilities given the limited understanding of the origin of dark energy (DE). It is a common understanding that the ISW effect adds to the power at the low multipoles of the CMB angular power spectrum. In this paper we carry out an analytic study to show that there are some expansion histories in which the ISW effect, instead of adding power, provides negative contribution to the power at low multipoles. Guided by the analytic study, we present examples of the features required in the late time expansion history of the universe that could explain the power deficiency through the ISW effect. We also show that an ISW origin of power deficiency is consistent, at present, with other cosmological observations that probe the expansion history such as distance modulus, matter power spectrum and the evolution of cluster number count. We also show that the ISW effect may be distinguished from power deficit originating from features in the PPS using the measurements of the CMB polarization spectrum at low multipoles expected from Planck. We conclude that the power at low multipoles of the CMB anisotropy could well be closely linked to Dark Energy puzzle in cosmology and this observation could be actually pointing to richer phenomenology of DE beyond the cosmological constant Λ.

  16. A multipole accelerated desingularized method for computing nonlinear wave forces on bodies

    SciTech Connect

    Scorpio, S.M.; Beck, R.F.

    1996-12-31

    Nonlinear wave forces on offshore structures are investigated. The fluid motion is computed using an Euler-Lagrange time domain approach. Nonlinear free surface boundary conditions are stepped forward in time using an accurate and stable integration technique. The field equation with mixed boundary conditions that result at each time step are solved at N nodes using a desingularized boundary integral method with multipole acceleration. Multipole accelerated solutions require O(N) computational effort and computer storage while conventional solvers require O(N{sup 2}) effort and storage for an iterative solution and O(N{sup 3}) effort for direct inversion of the influence matrix. These methods are applied to the three dimensional problem of wave diffraction by a vertical cylinder.

  17. Laser-Driven Fast Electron Collimation in Targets with Resistivity Boundary

    SciTech Connect

    Ramakrishna, B.; Kar, S.; Adams, D. J.; Markey, K.; Zepf, M.; Robinson, A. P. L.; Lancaster, K. L.; Green, J. S.; Norreys, P. A.; Quinn, M. N.; Yuan, X. H.; McKenna, P.; Scott, R. H. H.; Schreiber, J.

    2010-09-24

    We demonstrate experimentally that the relativistic electron flow in a dense plasma can be efficiently confined and guided in targets exhibiting a high-resistivity-core-low-resistivity-cladding structure analogous to optical waveguides. The relativistic electron beam is shown to be confined to an area of the order of the core diameter (50 {mu}m), which has the potential to substantially enhance the coupling efficiency of electrons to the compressed fusion fuel in the Fast Ignitor fusion in full-scale fusion experiments.

  18. AC conductivity scaling behavior in grain and grain boundary response regime of fast lithium ionic conductors

    NASA Astrophysics Data System (ADS)

    Mariappan, C. R.

    2014-05-01

    AC conductivity spectra of Li-analogues NASICON-type Li1.5Al0.5Ge1.5P3O12 (LAGP), Li-Al-Ti-P-O (LATP) glass-ceramics and garnet-type Li7La2Ta2O13 (LLTO) ceramic are analyzed by universal power law and Summerfield scaling approaches. The activation energies and pre-exponential factors of total and grain conductivities are following the Meyer-Neldel (M-N) rule for NASICON-type materials. However, the garnet-type LLTO material deviates from the M-N rule line of NASICON-type materials. The frequency- and temperature-dependent conductivity spectra of LAGP and LLTO are superimposed by Summerfield scaling. The scaled conductivity curves of LATP are not superimposed at the grain boundary response region. The superimposed conductivity curves are observed at cross-over frequencies of grain boundary response region for LATP by incorporating the exp ( {{{ - (EAt - EAg )} {{{ - (EAt - EAg )} {kT}}} ) factor along with Summerfield scaling factors on the frequency axis, where EAt and EAg are the activation energies of total and grain conductivities, respectively.

  19. A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh

    SciTech Connect

    Bauer, Carl A.; Werner, Gregory R.; Cary, John R.

    2013-10-15

    For embedded boundary electromagnetics using the Dey–Mittra (Dey and Mittra, 1997) [1] algorithm, a special grad–div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwell’s curl–curl matrix. Efficient curl–curl inversions are demonstrated within a shift-and-invert Krylov-subspace eigensolver (open-sourced at ([ofortt]https://github.com/bauerca/maxwell[cfortt])) on the spherical cavity and the 9-cell TESLA superconducting accelerator cavity. The accuracy of the Dey–Mittra algorithm is also examined: frequencies converge with second-order error, and surface fields are found to converge with nearly second-order error. In agreement with previous work (Nieter et al., 2009) [2], neglecting some boundary-cut cell faces (as is required in the time domain for numerical stability) reduces frequency convergence to first-order and surface-field convergence to zeroth-order (i.e. surface fields do not converge). Additionally and importantly, neglecting faces can reduce accuracy by an order of magnitude at low resolutions.

  20. Competing descriptions of diffusion profiles with two features: Surface space-charge layer versus fast grain-boundary diffusion

    NASA Astrophysics Data System (ADS)

    Schraknepper, H.; De Souza, R. A.

    2016-02-01

    Two different physical processes, (i) fast grain-boundary diffusion (FGBD) of oxygen and (ii) hindered oxygen diffusion in a surface space-charge layer, yield oxygen isotope diffusion profiles in a similar form. Two features are observed, with the short, sharp profile close to the surface being followed by a longer, shallower profile. In this study, we develop a procedure for deciding which of the two descriptions applies to experimentally measured profiles. Specifically, we solve Fick's second law, using finite-element simulations, to obtain oxygen isotope diffusion profiles for the two cases. Each set of profiles is then analysed in terms of the competing description. In this manner, we derive falsifiable conditions that allow physical processes to be assigned unambiguously to the two features of such isotope profiles. Applying these conditions to experimental profiles for SrTiO3 single crystals published in the literature, we find that FGBD is an invalid model for describing the diffusion processes.

  1. On reflecting boundary behind the Earth's orbit at propagation of fast particles from solar flares

    NASA Technical Reports Server (NTRS)

    Nishkovskikh, A. S.; Filippov, A. T.

    1985-01-01

    The flares of solar cosmic rays (SCR) associated with the presence of shocks in interplanetary magnetic field and with their propagation at significant heliocentric distances were always of great interest. Some events and problems concerning the peculiarities of propagation of flare CR in the interplanetary medium are considered. The distinguishing feature of such events is the presence of shock front behind the Earth's orbit having formed either directly in the process of shock generation on the Sun or at large heliocentric distances as a result of the interaction of fast and slow quasistationary recurrent solar wind (SW) streams. Based on the experimental material it is shown that the significant nonlinear disturbances in IMF behind the Earth's orbit can yield the occurrence of the additional SCR flux from shock front region as a result of the interaction of flare flux with shock and a partial reflection from it.

  2. Permanent multipole magnets with adjustable strength

    SciTech Connect

    Halbach, K.

    1983-03-01

    Preceded by a short discussion of the motives for using permanent magnets in accelerators, a new type of permanent magnet for use in accelerators is presented. The basic design and most important properties of a quadrupole will be described that uses both steel and permanent magnet material. The field gradient produced by this magnet can be adjusted without changing any other aspect of the field produced by this quadrupole. The generalization of this concept to produce other multipole fields, or combination of multipole fields, will also be presented.

  3. The Multipole Structure of Earth's STEP Signal

    NASA Technical Reports Server (NTRS)

    Nordtvedt, Kenneth

    2003-01-01

    If there is an interaction in physical law which differentially accelerates the test bodies in a STEP satellite, then the di.erent elements that compose the Earth will most likely have source strengths for this interaction which are not proportional to their mass densities. The rotational flattening of Earth and geographical irregularities of our planet's crust then produces a multipole structure for the Equivalence Principle violating force field which differs from the multipole structure of Earth's ordinary gravity field. Measuring these differences yields key information about the new interaction in physical law which is not attainable by solely measuring differences of test body accelerations.

  4. Thermal conductivity and resonant multipole interactions.

    NASA Technical Reports Server (NTRS)

    Nyeland, C.; Mason, E. A.; Monchick, L.

    1972-01-01

    Investigation of the influence of resonant multipole interactions on exchanges of rotational energy in molecular collisions, by means of a simple two-state impact-parameter approximation. It is found that dipole-quadrupole and quadrupole-quadrupole interactions can have a significant effect for molecules with low moments of inertia.

  5. Linearized multipole solutions and their representation

    NASA Astrophysics Data System (ADS)

    Hernández-Pastora, J. L.

    2013-09-01

    The monopole solution of the Einstein vacuum field equations (Schwarzschild’s solution) in Weyl coordinates involves a metric function that can be interpreted as the gravitational potential of a bar of length 2 m with constant linear density. The question addressed in this work is whether similar representations can be constructed for Weyl solutions other than the spherically symmetric one. A new family of static solutions of the axisymmetric vacuum field equations generalizing the M-Q(1) solution (Hernández-Pastora and Martín 1993 Class. Quantum Grav.10 2581) is developed. These represent slight deviations from spherical symmetry in terms of the relativistic multipole moments (RMM) we wish the solution to contain. A Newtonian object referred to as a dumbbell can be used to describe these solutions in a simple form by means of the density of this object, since the physical properties of the relativistic solution are characterized by its behaviour. The density profile of the dumbbell, which is given in terms of the RMM of the solution, allows us to distinguish general multipole Weyl solutions from the constant-density Schwarzschild solution. The range of values of the multipole moments that generate positive-definite density profiles is also calculated. The bounds on the multipole moments that arise from this density condition are identical to those required for a well-behaved infinite-redshift surface g00 = 0.

  6. Switched RC Multi-Pole Filter

    NASA Technical Reports Server (NTRS)

    Shuler, Robert L.

    1999-01-01

    The design and experimental verification of a switched RC multi-pole filter is presented. This highly compact circuit easily obtains sub-Hz, adjustable response utilizing reasonable sized on-chip components, and multiplexing the main resistor and op amp among filter stages. Design considerations for anti-aliasing, noise avoidance, and dynamic op amp compensation are presented.

  7. Vibrational solvatochromism and electrochromism. II. Multipole analysis.

    PubMed

    Lee, Hochan; Choi, Jun-Ho; Cho, Minhaeng

    2012-09-21

    Small infrared probe molecules have been widely used to study local electrostatic environment in solutions and proteins. Using a variety of time- and frequency-resolved vibrational spectroscopic methods, one can accurately measure the solvation-induced vibrational frequency shifts and the timescales and amplitudes of frequency fluctuations of such IR probes. Since the corresponding frequency shifts are directly related to the local electric field and its spatial derivatives of the surrounding solvent molecules or amino acids in proteins, one can extract information on local electric field around an IR probe directly from the vibrational spectroscopic results. Here, we show that, carrying out a multipole analysis of the solvatochromic frequency shift, the solvatochromic dipole contribution to the frequency shift is not always the dominant factor. In the cases of the nitrile-, thiocyanato-, and azido-derivatized molecules, the solvatochromic quadrupole contributions to the corresponding stretch mode frequency shifts are particularly large and often comparable to the solvatochromic dipole contributions. Noting that the higher multipole moment-solvent electric field interactions are short range effects in comparison to the dipole interaction, the H-bonding interaction-induced vibrational frequency shift can be caused by such short-range multipole-field interaction effects. We anticipate that the present multipole analysis method specifically developed to describe the solvatochromic vibrational frequency shifts will be useful to understand the intermolecular interaction-induced vibrational property changes and to find out a relationship between vibrational solvatochromism and electrochromism of IR probes in condensed phases. PMID:22998262

  8. Vibrational solvatochromism and electrochromism. II. Multipole analysis

    NASA Astrophysics Data System (ADS)

    Lee, Hochan; Choi, Jun-Ho; Cho, Minhaeng

    2012-09-01

    Small infrared probe molecules have been widely used to study local electrostatic environment in solutions and proteins. Using a variety of time- and frequency-resolved vibrational spectroscopic methods, one can accurately measure the solvation-induced vibrational frequency shifts and the timescales and amplitudes of frequency fluctuations of such IR probes. Since the corresponding frequency shifts are directly related to the local electric field and its spatial derivatives of the surrounding solvent molecules or amino acids in proteins, one can extract information on local electric field around an IR probe directly from the vibrational spectroscopic results. Here, we show that, carrying out a multipole analysis of the solvatochromic frequency shift, the solvatochromic dipole contribution to the frequency shift is not always the dominant factor. In the cases of the nitrile-, thiocyanato-, and azido-derivatized molecules, the solvatochromic quadrupole contributions to the corresponding stretch mode frequency shifts are particularly large and often comparable to the solvatochromic dipole contributions. Noting that the higher multipole moment-solvent electric field interactions are short range effects in comparison to the dipole interaction, the H-bonding interaction-induced vibrational frequency shift can be caused by such short-range multipole-field interaction effects. We anticipate that the present multipole analysis method specifically developed to describe the solvatochromic vibrational frequency shifts will be useful to understand the intermolecular interaction-induced vibrational property changes and to find out a relationship between vibrational solvatochromism and electrochromism of IR probes in condensed phases.

  9. Optimal Control by Multipoles in the Hele-Shaw Problem

    NASA Astrophysics Data System (ADS)

    Lokutsievskiy, Lev; Runge, Vincent

    2015-06-01

    The two-dimensional Hele-Shaw problem for a fluid spot with free boundary can be solved using the Polubarinova-Galin equation. The main condition of its applicability is the smoothness of the spot boundary. In the sink-case, this problem is not well-posed and the boundary loses smoothness within finite time—the only exception being the disk centred on the sink. An extensive literature deals with the study of the Hele-Shaw problem with non-smooth boundary or with surface tension, but the problem remains open. In our work, we propose to study this flow from a control point of view, by introducing an analogue of multipoles (term taken from the theory of electromagnetic fields). This allows us to control the shape of the spot and to avoid non-smoothness phenomenon on its border. For any polynomial contours, we demonstrate how all the fluid can be extracted, while the border remains smooth until the very end. We find, in particular, sufficient conditions for controllability and a link between Richardson's moments and Polubarinova-Galin equation.

  10. Multipole Analysis of Circular Cylindircal Magnetic Systems

    SciTech Connect

    J Selvaggi

    2006-01-09

    This thesis deals with an alternate method for computing the external magnetic field from a circular cylindrical magnetic source. The primary objective is to characterize the magnetic source in terms of its equivalent multipole distribution. This multipole distribution must be valid at points close to the cylindrical source and a spherical multipole expansion is ill-equipped to handle this problem; therefore a new method must be introduced. This method, based upon the free-space Green's function in cylindrical coordinates, is developed as an alternative to the more familiar spherical harmonic expansion. A family of special functions, called the toroidal functions or Q-functions, are found to exhibit the necessary properties for analyzing circular cylindrical geometries. In particular, the toroidal function of zeroth order, which comes from the integral formulation of the free-space Green's function in cylindrical coordinates, is employed to handle magnetic sources which exhibit circular cylindrical symmetry. The toroidal functions, also called Q-functions, are the weighting coefficients in a ''Fourier series-like'' expansion which represents the free-space Green's function. It is also called a toroidal expansion. This expansion can be directly employed in electrostatic, magnetostatic, and electrodynamic problems which exhibit cylindrical symmetry. Also, it is shown that they can be used as an alternative to the Elliptic integral formulation. In fact, anywhere that an Elliptic integral appears, one can replace it with its corresponding Q-function representation. A number of problems, using the toroidal expansion formulation, are analyzed and compared to existing known methods in order to validate the results. Also, the equivalent multipole distribution is found for most of the solved problems along with its corresponding physical interpretation. The main application is to characterize the external magnetic field due to a six-pole permanent magnet motor in terms of

  11. A model of magneto-electric multipoles.

    PubMed

    Lovesey, S W; Balcar, E

    2015-03-18

    A long-known Hamiltonian of electrons with entangled spin and orbital degrees of freedom is re-examined as a model of magneto-electric multipoles (MEs). In the model, a magnetic charge and simple quantum rotator are tightly locked in action, some might say they are enslaved entities. It is shown that MEs almost perfectly accord with those inferred from an analysis of magnetic neutron diffraction data on a ceramic superconductor (YBCO) in the pseudo-gap phase. Nigh on perfection between Stone's model and inferred MEs is achieved by addition to the original model of a crystal-field potential appropriate for the magnetic space group used in the published data analysis. An impression of thermal properties of multipoles is sought from a molecular-field model. PMID:25705914

  12. Poloidal OHMIC heating in a multipole

    SciTech Connect

    Holly, D.J.

    1982-01-01

    The feasibility of using poloidal currents to heat plasmas confined by a multipole field has been examined experimentaly in Tokapole II. The machine is operated as a toroidal octupole, with a time-varying toroidal magnetic field driving poloidal plasma currents I/sub plasma/ - 20 kA to give densities n/sub e/ - 10/sup 13/ cm/sup -3/ and temperatures T/sub e/ - 30 eV.

  13. Experiments in Planar Multipole Ion Traps

    NASA Astrophysics Data System (ADS)

    Clark, Rob; Burke, Timothy; Green, Dylan

    2016-05-01

    We present the design and demonstration of multipole ion traps based on concentric rings. We have developed both surface-electrode and layered planar trap designs which enable one to null the quadratic term in the electric potential to a high degree. Experiments demonstrating frequency upconversion of an applied signal demonstrate the nonlinear dynamics present in the trap. Applications include quantum chaos, ultracold chemistry, and, potentially, mass spectrometry. We acknowledge support from the Research Corporation for Science Advancement and from The Citadel Foundation.

  14. Revising the Multipole Moments of Numerical Spacetimes and its Consequences

    NASA Astrophysics Data System (ADS)

    Pappas, George; Apostolatos, Theocharis A.

    2012-06-01

    Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the object, and because the construction of a suitable analytic metric that mimics a numerical metric should be based on the multipole moments of the latter one in order to yield a reliable representation. In this Letter, we show that there has been a widespread delusion in the way the multipole moments of a numerical metric are read from the asymptotic expansion of the metric functions. We show how one should read correctly the first few multipole moments (starting from the quadrupole mass moment) and how these corrected moments improve the efficiency of describing the metric functions with analytic metrics that have already been used in the literature, as well as other consequences of using the correct moments.

  15. Collisionless spectral-kinetic Simulation of the Multipole Resonance Probe

    NASA Astrophysics Data System (ADS)

    Dobrygin, Wladislaw; Szeremley, Daniel; Schilling, Christian; Oberrath, Jens; Eremin, Denis; Mussenbrock, Thomas; Brinkmann, Ralf Peter

    2012-10-01

    Plasma resonance spectroscopy is a well established plasma diagnostic method realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development, which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation. In the simulation the potential is separeted in an inner and a vacuum potential. The inner potential is influenced by the charged partilces and is calculated by a specialized Poisson solver. The vacuum potential fulfills Laplace's equetion and consists of the applied voltage of the probe as boundary condition. Both potentials are expanded in spherical harmonics. For a practical particle pusher implementation, the expansion must be appropriately truncated. Compared to a PIC simulation a grid is unnecessary to calculate the force on the particles. This work purpose is a collisionless kinetic simulation, which can be used to investigate kinetic effects on the resonance behavior of the MRP.[4pt] [1] M. Lapke et al., Appl. Phys. Lett. 93, 2008, 051502.

  16. The reduced-cell multipole method for Ewald summations

    NASA Astrophysics Data System (ADS)

    Ding, Chris H. Q.

    1997-08-01

    The recently developed reduced-cell multipole method^1 (RCMM) for calculating electrostatic interactions in periodic systems is analyized and compared to the particle mesh Ewald method^2 (PME). RCMM reduces the distant millon atom unit cells into cells of 35 fictitious atoms on which the Ewald summations are trivially calculated and then combines them with the nearby unit cells via a varient of the fast multiple method (FMM). PME approximates the reciprocal space sum into a formulation with two FFTs. Accuracy in both methods can be systematically improved, although PME appear to be slightly better. Both scale like N*logN, but RCMM is better because Ewald summations on reduced-cell is entirely negligible. Overhead due to the system being periodic (vs. isolated system) is about 27Implementation of RCMM is simple modifications of an existing FMM for isolated systems; it is entirely new formulation for PME. 1. H.Q. Ding, et al., Chem.Phys.Lett. 196, 6 (1992); J.Chem.Phys. 97, 4309 (1992). 2. T. Darden, et al., J. Chem. Phys. 98, 10089 (1993); 103, 8577 (1995).

  17. GRID3O: Computer program for fast generation of multilevel, three-dimensional boundary-conforming O-type computational grids

    NASA Technical Reports Server (NTRS)

    Dulikravich, D. S.

    1981-01-01

    A fast algorithm was developed for accurately generating boundary-conforming, three-dimensional, consecutively refined computational grids applicable to arbitrary wing-body and axial turbomachinery geometries. The method is based on using an analytic function to generate two-dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These grids are of the O-type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flow field. Because the built-in nonorthogonal coordinate stretching and shearing cause the grid lines leaving the blade or wing trailing edge to end at downstream infinity, the numerical treatment of the three-dimensional trailing vortex sheets is simplified.

  18. Characterization of Multipole Microwave Cavity Filters

    NASA Astrophysics Data System (ADS)

    Reinhold, Philip; Schuster, David; Bishop, Lev S.

    2013-03-01

    An essential requirement for a quantum information processor is the ability to controllably couple and decouple individual qubits with each other. With superconducting circuit QED, this can be implemented by coupling multiple qubits to a transmission line cavity bus, and can be controlled by moving the qubit frequencies in and out of resonance with the bus. As coherence times increase, and the number of qubits attached to a bus grows larger, the problem of spurious coupling while detuned will become more important. We propose using principles from microwave filter design to create new couplers with higher contrast ratios in the effective qubit-qubit coupling. We present progress towards circuit implementations of multipole qubit coupling architectures.

  19. Stability of point-vortex multipoles revisited

    NASA Astrophysics Data System (ADS)

    Kizner, Ziv

    2011-06-01

    The point-vortex tripoles and pentapoles with zero total circulation are considered in the rigid-lid barotropic, equivalent-barotropic, and quasigeostrophic two-layer models. A tripole is assembled by three symmetrically arranged collinear vortices, while a pentapole by five vortices, of which one is located at the center of a square and four in the vertices of the square. The vortices on the sides, termed satellite vortices, are equal in strength and opposite in sign to the central vortex. To fulfill the zero-total-circulation condition, the central vortex is taken to be twice as strong as each of the satellite vortices in a tripole and four times as strong in a pentapole. In the two-layer model, two cases are distinguished, namely, the flat multipoles whose vortices are all located in the same layer and the carousel multipoles whose central vortex and satellite vortices reside in different layers. In all the models, the tripoles are shown to be nonlinearly stable and pentapoles, generally, unstable. Carousel pentapoles comparable in their size with the Rossby radius, and smaller, are exceptional in that they are stable to centrally symmetric perturbations (and, presumably, to arbitrary perturbations). The simple proof of the tripole stability is based on the fact that among the possible three-vortex configurations with zero total circulation characterized by the same (fixed) value of the Hamiltonian, there exists only one tripole, and, within the iso-Hamiltonian sheet, the squared linear momentum vanishes at this unique tripole only. This approach, being in essence universal for all models, works only with tripoles. For instance, a quadrupole cannot be treated in such a way, because there is a continuum of configurations of four vortices with zero total circulation on which the squared impulse vanishes. Dealing with pentapoles, we consider the perturbations that do not violate the central symmetry of the vortex configuration, fix the angular momentum, and examine

  20. Searching the Force Field Electrostatic Multipole Parameter Space.

    PubMed

    Jakobsen, Sofie; Jensen, Frank

    2016-04-12

    We show by tensor decomposition analyses that the molecular electrostatic potential for amino acid peptide models has an effective rank less than twice the number of atoms. This rank indicates the number of parameters that can be derived from the electrostatic potential in a statistically significant way. Using this as a guideline, we investigate different strategies for deriving a reduced set of atomic charges, dipoles, and quadrupoles capable of reproducing the reference electrostatic potential with a low error. A full combinatorial search of selected parameter subspaces for N-methylacetamide and a cysteine peptide model indicates that there are many different parameter sets capable of providing errors close to that of the global minimum. Among the different reduced multipole parameter sets that have low errors, there is consensus that atoms involved in π-bonding require higher order multipole moments. The possible correlation between multipole parameters is investigated by exhaustive searches of combinations of up to four parameters distributed in all possible ways on all possible atomic sites. These analyses show that there is no advantage in considering combinations of multipoles compared to a simple approach where the importance of each multipole moment is evaluated sequentially. When combined with possible weighting factors related to the computational efficiency of each type of multipole moment, this may provide a systematic strategy for determining a computational efficient representation of the electrostatic component in force field calculations. PMID:26925529

  1. Plasmon excitation in metal slab by fast point charge: The role of additional boundary conditions in quantum hydrodynamic model

    SciTech Connect

    Zhang, Ying-Ying; An, Sheng-Bai; Song, Yuan-Hong Wang, You-Nian; Kang, Naijing; Mišković, Z. L.

    2014-10-15

    We study the wake effect in the induced potential and the stopping power due to plasmon excitation in a metal slab by a point charge moving inside the slab. Nonlocal effects in the response of the electron gas in the metal are described by a quantum hydrodynamic model, where the equation of electronic motion contains both a quantum pressure term and a gradient correction from the Bohm quantum potential, resulting in a fourth-order differential equation for the perturbed electron density. Thus, besides using the condition that the normal component of the electron velocity should vanish at the impenetrable boundary of the metal, a consistent inclusion of the gradient correction is shown to introduce two possibilities for an additional boundary condition for the perturbed electron density. We show that using two different sets of boundary conditions only gives rise to differences in the wake potential at large distances behind the charged particle. On the other hand, the gradient correction in the quantum hydrodynamic model is seen to cause a reduction in the depth of the potential well closest to the particle, and a reduction of its stopping power. Even for a particle moving in the center of the slab, we observe nonlocal effects in the induced potential and the stopping power due to reduction of the slab thickness, which arise from the gradient correction in the quantum hydrodynamic model.

  2. Fast and selective determination of total protein in milk powder via titration of moving reaction boundary electrophoresis.

    PubMed

    Guo, Cheng-ye; Wang, Hou-yu; Liu, Xiao-ping; Fan, Liu-yin; Zhang, Lei; Cao, Cheng-xi

    2013-05-01

    In this paper, moving reaction boundary titration (MRBT) was developed for rapid and accurate quantification of total protein in infant milk powder, from the concept of moving reaction boundary (MRB) electrophoresis. In the method, the MRB was formed by the hydroxide ions and the acidic residues of milk proteins immobilized via cross-linked polyacrylamide gel (PAG), an acid-base indicator was used to denote the boundary motion. As a proof of concept, we chose five brands of infant milk powders to study the feasibility of MRBT method. The calibration curve of MRB velocity versus logarithmic total protein content of infant milk powder sample was established based on the visual signal of MRB motion as a function of logarithmic milk protein content. Weak influence of nonprotein nitrogen (NPN) reagents (e.g., melamine and urea) on MRBT method was observed, due to the fact that MRB was formed with hydroxide ions and the acidic residues of captured milk proteins, rather than the alkaline residues or the NPN reagents added. The total protein contents in infant milk powder samples detected via the MRBT method were in good agreement with those achieved by the classic Kjeldahl method. In addition, the developed method had much faster measuring speed compared with the Kjeldahl method. PMID:23483553

  3. Multipole moments of bumpy black holes

    SciTech Connect

    Vigeland, Sarah J.

    2010-11-15

    General relativity predicts the existence of black holes, compact objects whose spacetimes depend only on their mass, spin, and charge in vacuum (the 'no-hair' theorem). As various observations probe deeper into the strong fields of black hole candidates, it is becoming possible to test this prediction. Previous work suggested that such tests can be performed by measuring whether the multipolar structure of black hole candidates has the form that general relativity demands, and introduced a family of 'bumpy black hole' spacetimes to be used for making these measurements. These spacetimes have generalized multipoles, where the deviation from the Kerr metric depends on the spacetime's 'bumpiness'. In this paper, we show how to compute the Geroch-Hansen moments of a bumpy black hole, demonstrating that there is a clean mapping between the deviations used in the bumpy black hole formalism and the Geroch-Hansen moments. We also extend our previous results to define bumpy black holes whose current moments, analogous to magnetic moments of electrodynamics, deviate from the canonical Kerr value.

  4. Electromagnetic treatment of the multipole resonance probe

    NASA Astrophysics Data System (ADS)

    Lapke, Martin; Mussenbrock, Thomas; Brinkmann, Ralf Peter

    2009-10-01

    We present an electromagnetic model of the ``multipole resonance probe'' (MRP)-- a diagnostic concept which enables the simultaneous determination of plasma density, electron temperature, and collision rate in low-pressure gas discharges. The MRP is a radio-frequency driven probe of particular spherical design. In an idealized version the probe consists of two dielectrically shielded, conducting hemispheres. Driven by a radio-frequency source, the hemispheres are powered symmetrically. An analysis of the absorption spectrum shows a multitude of resonances, which allows for an analytical evaluation of the measured signal. The signal provides information on the distribution of the plasma in the probe's vicinity, from which the values of electron density, electron temperature and collision rate can be inferred. In this contribution the MRP will be modeled electromagnetically. Based on a comparision between full electromagnetic and electrostatic treatment, we show that a previously presented electrostatic treatment [1] was well justified.[4pt] [1] M.Lapke et al., Appl. Phys. Lett. 93, 051502 (2008)

  5. A fast Galerkin-based method for eigenfrequencies in acoustics of small rooms with slanted boundary planes

    NASA Astrophysics Data System (ADS)

    Sumbatyan, Mezhlum A.; Lannie, Michael Yu.; Zampoli, Vittorio

    2016-04-01

    This paper proposes a Galerkin-type numerical algorithm for an efficient calculation of low eigenfrequencies for rectangular parallelepiped rooms with slanted boundary planes, in the frequency interval (0 , 200) Hz, with the volume V ≤ 200m3. The main idea of the algorithm is to apply a system of Galerkin's basis functions which are orthogonal, after a certain change of variables, in a unit cube. As a result, the problem is reduced to a classical problem of the computational algebra about eigenvalues of a symmetric matrix. If applied to any parallelepiped of non-splayed geometry, the algorithm automatically gives the known classical modes. For rooms with the splayed planes, the sought mode frequencies can precisely be calculated in real time on a personal computer, by taking from 11 to 13 basis functions along each coordinate axis. Some particular examples are considered, in order to demonstrate the capability of the proposed algorithm, as well as its precision with a change of basis functions. It is also seen from the discussed examples that splaying the boundary planes can indeed make more uniform distribution of the low natural frequencies.

  6. Fast generation of three-dimensional computational boundary-conforming periodic grids of C-type. [for turbine blades and propellers

    NASA Technical Reports Server (NTRS)

    Dulikravich, D. S.

    1982-01-01

    A fast computer program, GRID3C, was developed to generate multilevel three dimensional, C type, periodic, boundary conforming grids for the calculation of realistic turbomachinery and propeller flow fields. The technique is based on two analytic functions that conformally map a cascade of semi-infinite slits to a cascade of doubly infinite strips on different Riemann sheets. Up to four consecutively refined three dimensional grids are automatically generated and permanently stored on four different computer tapes. Grid nonorthogonality is introduced by a separate coordinate shearing and stretching performed in each of three coordinate directions. The grids are easily clustered closer to the blade surface, the trailing and leading edges and the hub or shroud regions by changing appropriate input parameters. Hub and duct (or outer free boundary) have different axisymmetric shapes. A vortex sheet of arbitrary thickness emanating smoothly from the blade trailing edge is generated automatically by GRID3C. Blade cross sectional shape, chord length, twist angle, sweep angle, and dihedral angle can vary in an arbitrary smooth fashion in the spanwise direction.

  7. The China Clipper - Fast advective transport of radon-rich air from the Asian boundary layer to the upper troposphere near California

    NASA Technical Reports Server (NTRS)

    Kritz, Mark A.; Le Roulley, Jean-Claude; Danielsen, Edwin F.

    1990-01-01

    A series of upper tropospheric radon concentration measurements made over the eastern Pacific and west coast of the U.S. during the summers of 1983 and 1984 has revealed the occurrence of unexpectedly high radon concentrations for 9 of the 61 measurements. A frequency distribution plot of the set of 61 observations shows a distinct bimodal distribution, with approximately 2/5 of the observations falling close to 1 pCi/SCM, and 3/5 falling in a high concentration mode centered at about 11 pCi/SCM. Trajectory and synoptic analyses for two of the flights on which such high radon concentrations were observed indicate that this radon-rich air originated in the Asian boundary layer, ascended in cumulus updrafts, and was carried eastward in the fast moving air on the anticyclonic side of the upper tropospheric jet. The results suggest that the combination of rapid vertical transport from the surface boundary layer to the upper troposphere, followed by rapid horizontal transport eastward represents an efficient mode of long-transport for other, chemically reactive atmospheric trace constituents.

  8. Multipole moments of stellar oscillation modes

    NASA Technical Reports Server (NTRS)

    Reisenegger, Andreas

    1994-01-01

    The oscillating mass 2(exp l)-pole moment, M(sub nl), of a star in a given (normalized) oscillation mode determines the energy that can be absorbed by the mode in a tidal interaction and the power radiated by the mode in gravitational waves, both of which are proportional to (absolute value of M(sub nl))(exp 2). The coefficients in the expansion of the vector fields del(r(exp l)Y(sub lm)(theta, phi)) in terms of the displacement fields of modes of given l and m are proportional to M(sub nl). This expansion leads to a sum rule sum over n(absolute value of M(sub nl))(exp 2) = constant. For stars of weak to moderate central condensation (such as neutron stars), the f-mode is well approximated by the vector field being expanded, and therefore it takes the lion's share of the sum. Thus the multipole moments of all other modes must be small. In there numerical evaluation, it is necessary to know the shape of the eigenfunctions quite precisly, since a small f-mode contamination can significantly increase the obtained values. This contamination occurs in some `hybrid' numerical computations of neutron star oscillations with relativistic equilibrium stars and Newtonian dynamics (e.g., McDermott et al. 1988). In this case, it is due to a slight inconsistency in the models and leads to a large overestimate of the power radiated in gravitational waves by modes other than the f-mode, although their oscillation periods are nearly unaffected.

  9. Multipole expansion in plasmas: Effective interaction potentials between compound particles

    NASA Astrophysics Data System (ADS)

    Ramazanov, T. S.; Moldabekov, Zh. A.; Gabdullin, M. T.

    2016-05-01

    In this paper, the multipole expansion method is used to determine effective interaction potentials between particles in both classical dusty plasma and dense quantum plasma. In particular, formulas for interactions of dipole-dipole and charge-dipole pairs in a classical nondegenerate plasma as well as in degenerate quantum and semiclassical plasmas were derived. The potentials describe interactions between atoms, atoms and charged particles, dust particles in the complex plasma, atoms and electrons in the degenerate plasma, and metals. Correctness of the results obtained from the multipole expansion is confirmed by their agreement with the results based on other methods of statistical physics and dielectric response function. It is shown that the method of multipole expansion can be used to derive effective interaction potentials of compound particles, if the effect of the medium on the potential of individual particles comprising compound particles is known.

  10. Transferable Atomic Multipole Machine Learning Models for Small Organic Molecules.

    PubMed

    Bereau, Tristan; Andrienko, Denis; von Lilienfeld, O Anatole

    2015-07-14

    Accurate representation of the molecular electrostatic potential, which is often expanded in distributed multipole moments, is crucial for an efficient evaluation of intermolecular interactions. Here we introduce a machine learning model for multipole coefficients of atom types H, C, O, N, S, F, and Cl in any molecular conformation. The model is trained on quantum-chemical results for atoms in varying chemical environments drawn from thousands of organic molecules. Multipoles in systems with neutral, cationic, and anionic molecular charge states are treated with individual models. The models' predictive accuracy and applicability are illustrated by evaluating intermolecular interaction energies of nearly 1,000 dimers and the cohesive energy of the benzene crystal. PMID:26575759

  11. Application of multipole array sonic logging to acid hydralic fracturing

    NASA Astrophysics Data System (ADS)

    Tao, Guo; Gao, Kun; Wang, Bing; Ma, Yong

    2007-06-01

    Multipole array sonic logging tools have widely been employed in Chinese oilfields in recent years. We have developed a software package for rock mechanical analysis with multipole array sonic logs. This advanced data processing method and software have been applied to the Tahe oilfield in Northern West China to provide guidance to acid hydraulic fracturing design and evaluation. In this paper, we present the field examples of such data processing and applications to demonstrate the validity and advantages of our method and software package.

  12. Novel multipole Wien filter as three-dimensional spin manipulator

    SciTech Connect

    Yasue, T. Suzuki, M.; Koshikawa, T.; Tsuno, K.; Goto, S.; Arai, Y.

    2014-04-15

    Spin polarized electron beam is often used in material characterizations which relates to magnetism as well as in the high energy particle physics. The manipulation of the spin polarization toward the arbitrary direction is indispensable in such studies. In the present work, a novel multipole Wien filter is proposed as the three-dimensional spin manipulator, and a prototype 8-pole Wien filter is developed. It is applied to spin polarized low energy electron microscopy, and the variation of the magnetic contrast with managing the spin polarization is evaluated. It is confirmed that the novel multipole Wien filter can manipulate the spin polarization three-dimensionally.

  13. Multipole and plane wave expansions of diverging and converging fields.

    PubMed

    Hoang, Thanh Xuan; Chen, Xudong; Sheppard, Colin J R

    2014-04-21

    This paper presents and compares two basis systems, spherical harmonics and plane waves, for studying diverging and converging beams in an optical system. We show a similarity between a converging field and the time reversed field of a radiation field. We present and analyze the differences between the Debye-Wolf diffraction integral and the multipole theory for focusing of polarized light. The Debye-Wolf diffraction integral gives a well-known anomalous behavior on the optical axis and at the edge of the focused beam that can be avoided by using the multipole theory. PMID:24787784

  14. Design and characterization of combined function multipole magnet for accelerators

    SciTech Connect

    Sinha, Gautam; Singh, Gurnam

    2008-12-15

    This paper presents the design and analysis of a multipurpose combined function magnet for use in accelerators. This magnet consists of three corrector magnets: (i) skew quadrupole, (ii) horizontal dipole, and (iii) vertical dipole magnets, along with the main sextupole magnet. The strength of the corrector magnets is smaller than that of the main sextupole magnet. The strength of all the four magnets can be varied independently. The excitation strength required to produce skew quadrupole gradient and the presence of various multipole components in the magnet are estimated using first order perturbation theory. The experimental data for the variation of the sextupole strength and its higher order multipoles in the presence of skew quadrupole excitations are presented and compared to the theoretical predictions. Simulation using two-dimensional fine element code, Poisson, is also done. Results obtained from all the above three methods are found to be in good agreement with each other. The variations of skew quadrupole gradient for different sextupole excitations are also measured. The validity of this theory is also checked for various combinations of excitations including the case where magnet gets saturated. The excitation strengths required for producing the horizontal and vertical dipole fields are estimated analytically along with the presence of various multipoles. Theoretical predictions of permissible multipoles are compared to the results obtained from simulation.

  15. A Guide to Electronic Multipoles in Photon Scattering and Absorption

    NASA Astrophysics Data System (ADS)

    Lovesey, Stephen William; Balcar, Ewald

    2013-02-01

    The practice of replacing matrix elements in atomic calculations by those of convenient operators with strong physical appeal has a long history, and in condensed matter physics it is perhaps best known through use of operator equivalents in electron resonance by Elliott and Stevens. Likewise, electronic multipoles, created with irreducible spherical-tensors, to represent charge-like and magnetic-like quantities are widespread in modern physics. Examples in recent headlines include a magnetic charge (a monopole), an anapole (a dipole) and a triakontadipole (a magnetic-like atomic multipole of rank 5). In this communication, we aim to guide the reader through use of atomic, spherical multipoles in photon scattering, and resonant Bragg diffraction and dichroic signals in particular. Applications to copper oxide CuO and neptunium dioxide (NpO2) are described. In keeping with it being a simple guide, there is sparse use in the communication of algebra and expressions are gathered from the published literature and not derived, even when central to the exposition. An exception is a thorough grounding, contained in an Appendix, for an appropriate version of the photon scattering length based on quantum electrodynamics. A theme of the guide is application of symmetry in scattering, in particular constraints imposed on results by symmetry in crystals. To this end, a second Appendix catalogues constraints on multipoles imposed by symmetry in crystal point-groups.

  16. Two-dimensional multipole solitons in nonlocal nonlinear media.

    PubMed

    Rotschild, Carmel; Segev, Mordechai; Xu, Zhiyong; Kartashov, Yaroslav V; Torner, Lluis; Cohen, Oren

    2006-11-15

    We present the experimental observation of scalar multipole solitons in highly nonlocal nonlinear media, including dipole, tripole, quadrupole, and necklace-type solitons, organized as arrays of out-of-phase bright spots. These complex solitons are metastable, but with a large parameters range where the instability is weak, permitting their experimental observation. PMID:17072407

  17. Multipole moments for embedding potentials: Exploring different atomic allocation algorithms.

    PubMed

    S Nørby, Morten; Magnus Haugaard Olsen, Jógvan; Kongsted, Jacob; Aagard Jensen, Hans Jørgen

    2016-07-01

    Polarizable quantum mechanical (QM)/molecular mechanics (MM)-embedding methods are currently among the most promising methods for computationally feasible, yet reliable, production calculations of localized excitations and molecular response properties of large molecular complexes, such as proteins and RNA/DNA, and of molecules in solution. Our aim is to develop a computational methodology for distributed multipole moments and their associated multipole polarizabilities which is accurate, computationally efficient, and with smooth convergence with respect to multipole order. As the first step toward this goal, we herein investigate different ways of obtaining distributed atom-centered multipole moments that are used in the construction of the electrostatic part of the embedding potential. Our objective is methods that not only are accurate and computationally efficient, but which can be consistently extended with site polarizabilities including internal charge transfer terms. We present a new way of dealing with well-known problems in relation to the use of basis sets with diffuse functions in conventional atomic allocation algorithms, avoiding numerical integration schemes. Using this approach, we show that the classical embedding potential can be systematically improved, also when using basis sets with diffuse functions, and that very accurate embedding potentials suitable for QM/MM embedding calculations can be acquired. © 2016 Wiley Periodicals, Inc. PMID:27187063

  18. Real space electrostatics for multipoles. I. Development of methods

    NASA Astrophysics Data System (ADS)

    Lamichhane, Madan; Gezelter, J. Daniel; Newman, Kathie E.

    2014-10-01

    We have extended the original damped-shifted force (DSF) electrostatic kernel and have been able to derive three new electrostatic potentials for higher-order multipoles that are based on truncated Taylor expansions around the cutoff radius. These include a shifted potential (SP) that generalizes the Wolf method for point multipoles, and Taylor-shifted force (TSF) and gradient-shifted force (GSF) potentials that are both generalizations of DSF electrostatics for multipoles. We find that each of the distinct orientational contributions requires a separate radial function to ensure that pairwise energies, forces, and torques all vanish at the cutoff radius. In this paper, we present energy, force, and torque expressions for the new models, and compare these real-space interaction models to exact results for ordered arrays of multipoles. We find that the GSF and SP methods converge rapidly to the correct lattice energies for ordered dipolar and quadrupolar arrays, while the TSF is too severe an approximation to provide accurate convergence to lattice energies. Because real-space methods can be made to scale linearly with system size, SP and GSF are attractive options for large Monte Carlo and molecular dynamics simulations, respectively.

  19. Real space electrostatics for multipoles. I. Development of methods.

    PubMed

    Lamichhane, Madan; Gezelter, J Daniel; Newman, Kathie E

    2014-10-01

    We have extended the original damped-shifted force (DSF) electrostatic kernel and have been able to derive three new electrostatic potentials for higher-order multipoles that are based on truncated Taylor expansions around the cutoff radius. These include a shifted potential (SP) that generalizes the Wolf method for point multipoles, and Taylor-shifted force (TSF) and gradient-shifted force (GSF) potentials that are both generalizations of DSF electrostatics for multipoles. We find that each of the distinct orientational contributions requires a separate radial function to ensure that pairwise energies, forces, and torques all vanish at the cutoff radius. In this paper, we present energy, force, and torque expressions for the new models, and compare these real-space interaction models to exact results for ordered arrays of multipoles. We find that the GSF and SP methods converge rapidly to the correct lattice energies for ordered dipolar and quadrupolar arrays, while the TSF is too severe an approximation to provide accurate convergence to lattice energies. Because real-space methods can be made to scale linearly with system size, SP and GSF are attractive options for large Monte Carlo and molecular dynamics simulations, respectively. PMID:25296786

  20. Paleomagnetic records of core samples of the plate-boundary thrust drilled during the IODP Japan Trench Fast Drilling Project (JFAST)

    NASA Astrophysics Data System (ADS)

    Mishima, T.; Yang, T.; Ujiie, K.; Kirkpatrick, J. D.; Chester, F. M.; Moore, J. C.; Rowe, C. D.; Regalla, C.; Remitti, F.; Kameda, J.; Wolfson-Schwehr, M.; Bose, S.; Ishikawa, T.; Toy, V. G.

    2013-12-01

    IODP Expedition 343, Japan Trench Fast Drilling Project (JFAST), drilled across the plate-boundary décollement zone near the Japan Trench where large slip occurred during the March 2011 Tohoku-oki earthquake. We conducted paleomagnetic measurements of the core sample retrieved from the highly-deformed sediments comprising the plate-boundary décollement zone. Whole-round samples for structural analyses from five depth intervals of the core (0-12 cm, 12-30 cm, 43-48 cm, 48-58 cm, and 87.5-105 cm), were trimmed into oriented slabs with typical dimensions of 3x3x5 cm that are now being used to make petrographic sections for microstructural and chemical study. The remainder of the core sample was split into working and archive halves. We measured remanent magnetization of 16 trimmed slabs and the archive half of the core sample. The slabs were subjected to natural remanent magnetization (NRM) measurements in 0.5-1 cm intervals and progressive alternating field demagnetization (AFD) up to 80 mT with a 2G755 pass-through superconducting rock magnetometer at Kochi University. The archive half of the core sample was subjected to NRM measurement and AFD up to 20 mT with a 2G760 superconducting rock magnetometer installed on R/V Chikyu. Typically, two or three paleomagnetic components were isolated during the AFD of slab samples up to 80 mT. One ';soft' component was demagnetized below 20-30 mT, and another ';hard' component was not demagnetized even with AFD in 80 mT. A third component may be separated during AFD at the intermediate demagnetizing field, and may overlap the soft and hard components. The multiple slab samples cut from an identical whole-round sample have generally consistent paleomagnetic direction of the hard component. Contrastingly, the direction of the soft component is less consistent between adjacent slabs, and even varies within a single slab. The direction variation of the soft component possibly reflects the cm-scale strain and rotation of the

  1. Measurements of diurnal variations and eddy covariance (EC) fluxes of glyoxal in the tropical marine boundary layer: description of the Fast LED-CE-DOAS instrument

    NASA Astrophysics Data System (ADS)

    Coburn, S.; Ortega, I.; Thalman, R.; Blomquist, B.; Fairall, C. W.; Volkamer, R.

    2014-10-01

    Here we present first eddy covariance (EC) measurements of fluxes of glyoxal, the smallest α-dicarbonyl product of hydrocarbon oxidation, and a precursor for secondary organic aerosol (SOA). The unique physical and chemical properties of glyoxal - i.e., high solubility in water (effective Henry's law constant, KH = 4.2 × 105 M atm-1) and short atmospheric lifetime (~2 h at solar noon) - make it a unique indicator species for organic carbon oxidation in the marine atmosphere. Previous reports of elevated glyoxal over oceans remain unexplained by atmospheric models. Here we describe a Fast Light-Emitting Diode Cavity-Enhanced Differential Optical Absorption Spectroscopy (Fast LED-CE-DOAS) instrument to measure diurnal variations and EC fluxes of glyoxal and inform about its unknown sources. The fast in situ sensor is described, and first results are presented from a cruise deployment over the eastern tropical Pacific Ocean (20° N to 10° S; 133 to 85° W) as part of the Tropical Ocean tRoposphere Exchange of Reactive halogens and Oxygenated VOCs (TORERO) field experiment (January to March 2012). The Fast LED-CE-DOAS is a multispectral sensor that selectively and simultaneously measures glyoxal (CHOCHO), nitrogen dioxide (NO2), oxygen dimers (O4), and water vapor (H2O) with ~2 Hz time resolution (Nyquist frequency ~1 Hz) and a precision of ~40 pptv Hz-0.5 for glyoxal. The instrument is demonstrated to be a "white-noise" sensor suitable for EC flux measurements. Fluxes of glyoxal are calculated, along with fluxes of NO2, H2O, and O4, which are used to aid the interpretation of the glyoxal fluxes. Further, highly sensitive and inherently calibrated glyoxal measurements are obtained from temporal averaging of data (e.g., detection limit smaller than 2.5 pptv in an hour). The campaign average mixing ratio in the Southern Hemisphere (SH) is found to be 43 ± 9 pptv glyoxal, which is higher than the Northern Hemisphere (NH) average of 32 ± 6 pptv (error reflects

  2. Complex multipole beam approach to electromagnetic scattering problems

    NASA Astrophysics Data System (ADS)

    Mittra, Raj; Boag, Amir

    1994-03-01

    A novel approach to reducing the matrix size associated with the Method of Moments (MoM) solution of the problem of electromagnetic scattering from arbitrary shaped closed bodies is presented in this paper. The key step in this approach is to represent the scattered field in terms of a series of beams produced by multipole sources resemble the Gabor basis functions. By utilizing the properties of the Gabor series, guidelines for selecting the orders as well as locations of the multipole sources are developed. It is shown that the present approach not only reduces the number of unknowns, but also generates a generalized impedance matrix with a banded structure and a low condition number. The accuracy of the proposed method is verified by comparing the numerical results with those derived by using the method of moments.

  3. MEASUREMENT OF MULTIPOLE STRENGTHS FROM RHIC BPM DATA.

    SciTech Connect

    TOMAS,R.BAI,M.FISCHER,W.ET AL.

    2004-07-05

    Recently resonance driving terms were successfully measured in the CERN SPS and the BNL RHIC from the Fourier spectrum of BPM data. Based on these measurements a new analysis has been derived to extract multipole strengths. In this paper we present experimental measurements of sextupolar and skew quadrupolar strengths carried out at RHIC. A non-destructive measurement using an AC dipole is also presented.

  4. The multipole resonance probe: characterization of a prototype

    NASA Astrophysics Data System (ADS)

    Lapke, Martin; Oberrath, Jens; Schulz, Christian; Storch, Robert; Styrnoll, Tim; Zietz, Christian; Awakowicz, Peter; Brinkmann, Ralf Peter; Musch, Thomas; Mussenbrock, Thomas; Rolfes, Ilona

    2011-08-01

    The multipole resonance probe (MRP) was recently proposed as an economical and industry compatible plasma diagnostic device (Lapke et al 2008 Appl. Phys. Lett. 93 051502). This communication reports the experimental characterization of a first MRP prototype in an inductively coupled argon/nitrogen plasma at 10 Pa. The behavior of the device follows the predictions of both an analytical model and a numerical simulation. The obtained electron densities are in excellent agreement with the results of Langmuir probe measurements.

  5. Closed expressions for the magnetic field of toroidal multipole configurations

    SciTech Connect

    Sheffield, G.V.

    1983-04-01

    Closed analytic expressions for the vector potential and the magnetic field for the lower order toroidal multipoles are presented. These expressions can be applied in the study of tokamak plasma cross section shaping. An example of such an application is included. These expressions also allow the vacuum fields required for plasma equilibrium to be specified in a general form independent of a particular coil configuration.

  6. Multipole moments for black objects in five dimensions

    SciTech Connect

    Tanabe, Kentaro; Ohashi, Seiju; Shiromizu, Tetsuya

    2010-11-15

    In higher dimensions than four, conventional uniqueness theorem in asymptotically flat space-times does not hold, i.e., black objects cannot be classified only by the mass, angular momentum, and charge. In this paper, we define multipole moments for black objects and show that Myers-Perry black hole and black ring can be distinguished by quadrupole moments. This consideration gives us a new insight for the uniqueness theorem for black objects in higher dimensions.

  7. Multipole gas thruster design. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Isaacson, G. C.

    1977-01-01

    The development of a low field strength multipole thruster operating on both argon and xenon is described. Experimental results were obtained with a 15-cm diameter multipole thruster and are presented for a wide range of discharge-chamber configurations. Minimum discharge losses were 300-350 eV/ion for argon and 200-250 eV/ion for xenon. Ion beam flatness parameters in the plane of the accelerator grid ranged from 0.85 to 0.93 for both propellants. Thruster performance is correlated for a range of ion chamber sizes and operating conditions as well as propellant type and accelerator system open area. A 30-cm diameter ion source designed and built using the procedure and theory presented here-in is shown capable of low discharge losses and flat ion-beam profiles without optimization. This indicates that by using the low field strength multipole design, as well as general performance correlation information provided herein, it should be possible to rapidly translate initial performance specifications into easily fabricated, high performance prototypes.

  8. Development of a multi-pole magnetorheological brake

    NASA Astrophysics Data System (ADS)

    Shiao, Yaojung; Nguyen, Quang-Anh

    2013-06-01

    This paper presents a new approach in the design and optimization of a novel multi-pole magnetorheological (MR) brake that employs magnetic flux more effectively on the surface of the rotor. MR brakes with conventional single ring-type electromagnetic poles have reached the limits of torque enhancement. One major reason is the limitation of the magnetic field strength within the active area of the MR fluid due to the geometric constraints of the coil. The multi-pole MR brake design features multiple electromagnetic poles surrounded by several coils. As a result, the active chaining areas for the MR fluid are greatly increased, and significant brake torque improvement is achieved. The coil structure, as a part of the stator, becomes flexible and customizable in terms of space usage for the winding and bobbin design. In addition, this brake offers extra options in its dimensions for torque enhancement because either the radial or the axial dimensions of the rotor can be increased. Magnetic circuit analysis was conducted to analyze the effects of the design parameters on the field torque. After that, simulations were done to find the optimal design under all major geometric constraints with a given power supply. The results show that the multi-pole MR brake provides a considerable braking torque increase while maintaining a compact and solid design. This is confirmation of its feasibility in actual braking applications.

  9. Coarse-graining the electrostatic potential via distributed multipole expansions

    PubMed Central

    Gramada, Apostol; Bourne, Philip E.

    2011-01-01

    Multipole expansions offer a natural path to coarse-graining the electrostatic potential. However, the validity of the expansion is restricted to regions outside a spherical enclosure of the distribution of charge and, therefore, not suitable for most applications that demand accurate representation at arbitrary positions around the molecule. We propose and demonstrate a distributed multipole expansion approach that resolves this limitation. We also provide a practical algorithm for the computational implementation of this approach. The method allows the partitioning of the charge distribution into subsystems so that the multipole expansion of each component of the partition, and therefore of their superposition, is valid outside an enclosing surface of the molecule of arbitrary shape. The complexity of the resulting coarse-grained model of electrostatic potential is dictated by the area of the molecular surface and therefore, for a typical three-dimensional molecule, it scale as N2/3 with N, the number of charges in the system. This makes the method especially useful for coarse-grained studies of biological systems consisting of many large macromolecules provided that the configuration of the individual molecules can be approximated as fixed. PMID:21572587

  10. Generalization of the Gaussian electrostatic model: Extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods

    PubMed Central

    Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.

    2007-01-01

    The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15 kcal/mol error for

  11. Generalization of the Gaussian electrostatic model: Extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods

    NASA Astrophysics Data System (ADS)

    Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.

    2006-11-01

    The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15kcal/mol error for

  12. Cluster-Based Multipolling Sequencing Algorithm for Collecting RFID Data in Wireless LANs

    NASA Astrophysics Data System (ADS)

    Choi, Woo-Yong; Chatterjee, Mainak

    2015-03-01

    With the growing use of RFID (Radio Frequency Identification), it is becoming important to devise ways to read RFID tags in real time. Access points (APs) of IEEE 802.11-based wireless Local Area Networks (LANs) are being integrated with RFID networks that can efficiently collect real-time RFID data. Several schemes, such as multipolling methods based on the dynamic search algorithm and random sequencing, have been proposed. However, as the number of RFID readers associated with an AP increases, it becomes difficult for the dynamic search algorithm to derive the multipolling sequence in real time. Though multipolling methods can eliminate the polling overhead, we still need to enhance the performance of the multipolling methods based on random sequencing. To that extent, we propose a real-time cluster-based multipolling sequencing algorithm that drastically eliminates more than 90% of the polling overhead, particularly so when the dynamic search algorithm fails to derive the multipolling sequence in real time.

  13. Effective multipoles and Yukawa electrostatics in dressed molecule theory

    NASA Astrophysics Data System (ADS)

    Ramirez, Rosa; Kjellander, Roland

    2006-10-01

    In this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from "dressed molecule theory" to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of many-body correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, exp(-κr )/r, where r is the distance and 1/κ is the decay length (it is normally different from the Debye length). The resulting "Yukawa electrostatics" differ in many respects from ordinary, unscreened electrostatics. The "Yukawa charge" of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large r. As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large r values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the Poisson-Boltzmann approximation for primitive model electrolytes.

  14. Effective multipoles and Yukawa electrostatics in dressed molecule theory.

    PubMed

    Ramirez, Rosa; Kjellander, Roland

    2006-10-14

    In this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from "dressed molecule theory" to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of many-body correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, exp(-kappa r)/r, where r is the distance and 1/kappa is the decay length (it is normally different from the Debye length). The resulting "Yukawa electrostatics" differ in many respects from ordinary, unscreened electrostatics. The "Yukawa charge" of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large r. As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large r values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the Poisson-Boltzmann approximation for primitive model electrolytes. PMID:17042582

  15. Investigation of Multipole Electrostatics in Hydration Free Energy Calculations

    PubMed Central

    Shi, Yue; Wu, Chuanjie; Ponder, Jay W.; Ren, Pengyu

    2010-01-01

    Hydration free energy (HFE) is generally used for evaluating molecular solubility, which is an important property for pharmaceutical and chemical engineering processes. Accurately predicting HFE is also recognized as one fundamental capability of molecular mechanics force field. Here we present a systematic investigation on HFE calculations with AMOEBA polarizable force field at various parameterization and simulation conditions. The HFEs of seven small organic molecules have been obtained alchemically using the Bennett Acceptance Ratio (BAR) method. We have compared two approaches to derive the atomic multipoles from quantum mechanical (QM) calculations: one directly from the new distributed multipole analysis (DMA) and the other involving fitting to the electrostatic potential around the molecules. Wave functions solved at the MP2 level with four basis sets (6-311G*, 6-311++G(2d,2p), cc-pVTZ, and aug-cc-pVTZ) are used to derive the atomic multipoles. HFEs from all four basis sets show a reasonable agreement with experimental data (root mean square error 0.63 kcal/mol for aug-ccpVTZ). We conclude that aug-cc-pVTZ gives the best performance when used with AMOEBA, and 6-311++G(2d,2p) is comparable but more efficient for larger systems. The results suggest that the inclusion of diffuse basis functions is important for capturing intermolecular interactions. The effect of long-range correction to van der Waals interaction on the hydration free energies is about 0.1 kcal/mol when the cutoff is 12Å, and increases linearly with the number of atoms in the solute/ligand. In addition, we also discussed the results from a hybrid approach that combines polarizable solute with fixed-charge water in the hydration free energy calculation. PMID:20925089

  16. Analytical expressions for fringe fields in multipole magnets

    NASA Astrophysics Data System (ADS)

    Muratori, B. D.; Jones, J. K.; Wolski, A.

    2015-06-01

    Fringe fields in multipole magnets can have a variety of effects on the linear and nonlinear dynamics of particles moving along an accelerator beam line. An accurate model of an accelerator must include realistic models of the magnet fringe fields. Fringe fields for dipoles are well understood and can be modeled at an early stage of accelerator design in such codes as mad8, madx, gpt or elegant. Existing techniques for quadrupole and higher order multipoles rely either on the use of a numerical field map, or on a description of the field in the form of a series expansion about a chosen axis. Usually, it is not until the later stages of a design project that such descriptions (based on magnet modeling or measurement) become available. Furthermore, series expansions rely on the assumption that the beam travels more or less on axis throughout the beam line; but in some types of machines (for example, Fixed Field Alternating Gradients or FFAGs) this is not a good assumption. Furthermore, some tracking codes, such as gpt, use methods for including space charge effects that require fields to vary smoothly and continuously along a beam line: in such cases, realistic fringe field models are of significant importance. In this paper, a method for constructing analytical expressions for multipole fringe fields is presented. Such expressions allow fringe field effects to be included in beam dynamics simulations from the start of an accelerator design project, even before detailed magnet design work has been undertaken. The magnetostatic Maxwell equations are solved analytically and a solution that fits all orders of multipoles is derived. Quadrupole fringe fields are considered in detail as these are the ones that give the strongest effects. The analytic expressions for quadrupole fringe fields are compared with data obtained from numerical modeling codes in two cases: a magnet in the high luminosity upgrade of the Large Hadron Collider inner triplet, and a magnet in the

  17. Optics in the Multipole Approximation: From Atomic Systems to Solids

    SciTech Connect

    CHOW, WENG W.; KNORR, ANDREAS; KOCH, STEPHAN W.

    1999-09-13

    Starting from the microscopic light-matter interaction in form of the minimal coupling Hamiltonian, the multipole approximation for the optical response of localized electrons in atomic systems is extended to delocalized electrons in solids. A spatial averaging procedure is used to derive the electromagnetic sources for macroscopic Maxwell's equations as well as the corresponding many particle Hamiltonian on a coarse grained length scale. The results are illustrated for semiconductor bulk material up to quadruple moments for the interband transitions, where gauge invariant equations of motion for the optical response are obtained.

  18. Tests of planar permanent magnet multipole focusing elements

    SciTech Connect

    Cobb, J.; Tatchyn, R.

    1993-08-01

    In recent work, planar configurations of permanent magnets were proposed as substitutes for conventional current-driven iron quadrupoles in applications limited by small aperture sizes and featuring small beam occupation diameters. Important examples include the configuring of focusing lattices in small-gap insertion devices, and the implementation of compact mini-beta sections on linear or circular machines. In subsequent analysis, this approach was extended to sextupoles and higher-order multipoles. In this paper we report on initial measurements conducted at the Stanford Linear Accelerator Center on recently fabricated planar permanent magnet quadrupoles and sextupoles configured out of SmCo and NdFe/B.

  19. Experimental demonstration of a surface-electrode multipole ion trap

    NASA Astrophysics Data System (ADS)

    Maurice, Mark; Allen, Curtis; Green, Dylan; Farr, Andrew; Burke, Timothy; Hilleke, Russell; Clark, Robert

    2015-08-01

    We report on the design and experimental characterization of a surface-electrode multipole ion trap. Individual microscopic sugar particles are confined in the trap. The trajectories of driven particle motion are compared with a theoretical model, both to verify qualitative predictions of the model and to measure the charge-to-mass ratio of the confined particle. The generation of harmonics of the driving frequency is observed as a key signature of the nonlinear nature of the trap. We remark on possible applications of our traps, including to mass spectrometry.

  20. Dipole and higher multipole particle creation in the steady state universe

    NASA Astrophysics Data System (ADS)

    Liboff, Richard L.

    1994-08-01

    The birth of a particle in an otherwise empty universe is studied. The particle is a sphere is a sphere of radius a, with unifrom mass density and surface charge density corresponding to a point dipole p, at the origin. Consistent with equsions of general relativity and Maxwell's equations, gravity and dipole fields propagate away from the particle's initiation with the speed of light. Field energies are supplied by the particle's mass which subsequently decays in time. Asmotic solution to a nonlinear equation for the remaining mass gives the following criterion for the mass to survive the expanding fields: mzero c2 greater than u p, where up is identically = p2/3a3 is the self-energy of the dipole particle. A similar relation is derived for all higher order multipole particles resulting in a parallel inequality with u p replaced by the self-energy of the multipole particle. In all such events, from the monopole to all higher multipole particles, it is found that if the multipole component of self-energy is equated to the starting rest-mass energy of the particle, then the final stae of the system includes a massless multipole particle with its corresponding multipole potential field. As such particles are not observed in nature, it is concluded that for consistency of the steady state universe, the starting rest mass of a multipole particle must exceed the multipole component of its self-energy.

  1. Artificially Structured Boundary For Antihydrogen Studies

    SciTech Connect

    Ordonez, C. A.

    2011-06-01

    It may be possible to confine antiprotons using an artificially structured boundary, as part of a process for synthesizing antihydrogen. An artificially structured boundary is defined at present as one that produces a spatially periodic static field, such that the spatial period and range of the field is much smaller than the dimensions of a cloud, plasma or beam of charged particles that is confined by the boundary. A modified Kingdon trap could employ an artificially structured boundary at the location of inner electrodes. The artificially structured boundary would produce a multipole magnetic field that keeps confined particles from reaching the inner electrodes. The magnetic field would be sufficiently short in range to affect the particle trajectories only in close proximity to the inner electrodes. The conditions for producing such a magnetic field have been assessed. The results indicate that the magnetic field must be an octupole or higher order field.

  2. Rogue Mode Shileding in NSLS-II Multipole Vacuum Chambers

    SciTech Connect

    Ferreira, M.; Blednykh, A.; Bacha, B.; Borrelli, A.; Hseuh, H.-C.; Kosciuk, B.; Krinsky, S.; Singh, O.; Vetter, K.

    2011-03-28

    Modes with transverse electric field (TE-modes) in the NSLS-II multipole vacuum chamber can be generated at frequencies above 450MHz due to its geometric dimensions. Since the NSLS-II BPM system monitors signals within 10 MHz band at RF frequency of 500 MHz, frequencies of higher-order modes (HOM) can be generated within the transmission band of the band pass filter. In order to avoid systematic errors in the NSLS-II BPM system, we introduced frequency shift of HOMs by using RF metal shielding located in the antechamber slot. We demonstrated numerical modeling and experimental studies of the spurious TE modes in the NSLS-II vacuum chambers with antechamber slot. Calculated frequencies of TE-modes in considered chambers with and without RF shielding were verified experimentally. Flexible BeCu RF shielding inside each chamber at proper location shifts frequencies of H{sub 10p}-modes above {approx}900MHz, except chambers S6 odd and even. These chambers need special attention because of synchrotron radiation from downstream magnets. S6 odd multipole vacuum chamber needs to be measured and the RF shielding length has to be optimized. RF shielding looks adequate for baseline design. Fifty percent of open space provides adequate pumping speed.

  3. Multipole mixing ratios and substate populations in Rn-219

    NASA Astrophysics Data System (ADS)

    Jones, G. D.

    2016-08-01

    Historical alpha-gamma angular correlation data for the decay of 223Ra into excited states of 219Rn have been analysed, using the correct spins of the states involved, for the first time. The analyses produced multipole mixing ratios (E2/M1) of δ (144)=-0.11\\+/- 0.03, δ (154)=0, δ (158)=-0.205\\+/- 0.018 and δ (269)=-0.149\\+/- 0.004 where the nominal transition energies, in keV, are given in brackets. These values are consistent with published values obtained from internal conversion electron spectroscopy. It is also found that δ (324)=0 and δ (338)=-0.235\\+/- 0.030 (where both values differ from current tabulations) and that the sign of the multipole mixing ratio for the 122 keV transition is negative. The 158, 269 and 338 keV states are found to be aligned with high population of M=+/- 3/2 substates and the 127 keV state is believed to have undergone spin relaxation.

  4. CMB multipole measurements in the presence of foregrounds

    NASA Astrophysics Data System (ADS)

    de Oliveira-Costa, Angélica; Tegmark, Max

    2006-07-01

    Most analysis of cosmic microwave background spherical harmonic coefficients aℓm has focused on estimating the power spectrum Cℓ=⟨|aℓm|2⟩ rather than the coefficients themselves. We present a minimum-variance method for measuring aℓm given anisotropic noise, incomplete sky coverage and foreground contamination, and apply it to the Wilkinson Microwave Anisotropy Probe (WMAP) data. Our method is shown to constitute lossless data compression in the sense that the widely used quadratic estimators of the power spectrum Cℓ can be computed directly from our aℓm-estimators. As the Galactic cut is increased, the error bars Δaℓm on low multipoles go from being dominated by foregrounds to being dominated by leakage from other multipoles, with the intervening minimum defining the optimal cut. Applying our method to the WMAP quadrupole and octopole as an illustration, we investigate the robustness of the previously reported “axis of evil” alignment to Galactic cut and foreground contamination.

  5. A Multipole Expansion Method for Analyzing Lightning Field Changes

    NASA Technical Reports Server (NTRS)

    Koshak, William J.; Krider, E. Philip; Murphy, Martin J.

    1998-01-01

    Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q-model) or a point dipole (the P-model). The Q-model has 4 unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P-model has 6 unknown parameters and describes many intracloud (IC) discharges. In this paper, we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a 3-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer simulated sources and on natural lightning at the NASA Kennedy Space Center and USAF Eastern Range.

  6. A Multipole Expansion Method for Analyzing Lightning Field Changes

    NASA Technical Reports Server (NTRS)

    Koshak, William J.; Krider, E. Philip; Murphy, Martin J.

    1999-01-01

    Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q model) or a point dipole (the P model). The Q model has four unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P model has six unknown parameters and describes many intracloud (IC) discharges. In this paper we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a dme-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer-simulated sources and on natural lightning at the NASA Kennedy Space Center and U.S. Air Force Eastern Range.

  7. Vanadium magnetoelectric multipoles in V2O3

    NASA Astrophysics Data System (ADS)

    Lovesey, S. W.; Fernández-Rodríguez, J.; Blanco, J. A.; Sivia, D. S.; Knight, K. S.; Paolasini, L.

    2007-01-01

    We establish the contributions made by the vanadium anapole, and other magnetoelectric multipoles, to the electron ground state of V2O3 in its antiferromagnetic modification. To this end, observations made by resonant x-ray Bragg diffraction are analyzed in terms of a scattering amplitude derived within the atomic model. The amplitude is a coherent sum of E1-E2 and E2-E2 resonance events that is fully compliant with the established chemical (I2/a) and magnetic space groups. One set of values for the V multipoles are found to give a totally satisfactory account of all data collected at two space-group forbidden Bragg reflections in the two polarization channels σ'σ and π'σ ( σ primary polarization, and σ' and π' secondary polarizations). Derived estimates of the V anapole (E1-E2) and V octupole (E2-E2) are good to within a few percent, and the E1-E2 event alone is shown not to adequately describe the diffraction data.

  8. Polarizable Atomic Multipole-based Molecular Mechanics for Organic Molecules

    PubMed Central

    Ren, Pengyu; Wu, Chuanjie; Ponder, Jay W.

    2011-01-01

    An empirical potential based on permanent atomic multipoles and atomic induced dipoles is reported for alkanes, alcohols, amines, sulfides, aldehydes, carboxylic acids, amides, aromatics and other small organic molecules. Permanent atomic multipole moments through quadrupole moments have been derived from gas phase ab initio molecular orbital calculations. The van der Waals parameters are obtained by fitting to gas phase homodimer QM energies and structures, as well as experimental densities and heats of vaporization of neat liquids. As a validation, the hydrogen bonding energies and structures of gas phase heterodimers with water are evaluated using the resulting potential. For 32 homo- and heterodimers, the association energy agrees with ab initio results to within 0.4 kcal/mol. The RMS deviation of hydrogen bond distance from QM optimized geometry is less than 0.06 Å. In addition, liquid self-diffusion and static dielectric constants computed from molecular dynamics simulation are consistent with experimental values. The force field is also used to compute the solvation free energy of 27 compounds not included in the parameterization process, with a RMS error of 0.69 kcal/mol. The results obtained in this study suggest the AMOEBA force field performs well across different environments and phases. The key algorithms involved in the electrostatic model and a protocol for developing parameters are detailed to facilitate extension to additional molecular systems. PMID:22022236

  9. Cell multipole method for molecular simulations in bulk and confined systems

    SciTech Connect

    Zheng, Jie; Balasundaram, Ramkumar; Gehrke, Stevin H.; Heffelfinger, Grant S.; Goddard, William A. III; Jiang, Shaoyi

    2002-08-01

    One of the bottlenecks in molecular simulations is to treat large systems involving electrostatic interactions. Computational time in conventional molecular simulation methods scales with O(N{sup 2}), where N is the number of atoms. With the emergence of the cell multipole method (CMM) and massively parallel supercomputers, simulations of 10 million atoms have been performed. In this work, the optimal hierarchy cell level and the algorithm for Taylor expansion were recommended for fast and accurate molecular dynamics (MD) simulations of three-dimensional (3D) systems. CMM was then extended to treat quasi-two-dimensional (2D) systems, which is very important for condensed matter physics problems. In addition, CMM was applied to grand canonical ensemble Monte Carlo (GCMC) simulations for both 3D and 2D systems. Under the optimal conditions, the results show that computational time is approximately linear with N for large systems, average error in total potential energy is less than {approx}1%, and RMS force is about 0.015 for 3D and 2D systems when compared with the Ewald summation.

  10. Magnetic assembly of colloidal superstructures with multipole symmetry.

    PubMed

    Erb, Randall M; Son, Hui S; Samanta, Bappaditya; Rotello, Vincent M; Yellen, Benjamin B

    2009-02-19

    The assembly of complex structures out of simple colloidal building blocks is of practical interest for building materials with unique optical properties (for example photonic crystals and DNA biosensors) and is of fundamental importance in improving our understanding of self-assembly processes occurring on molecular to macroscopic length scales. Here we demonstrate a self-assembly principle that is capable of organizing a diverse set of colloidal particles into highly reproducible, rotationally symmetric arrangements. The structures are assembled using the magnetostatic interaction between effectively diamagnetic and paramagnetic particles within a magnetized ferrofluid. The resulting multipolar geometries resemble electrostatic charge configurations such as axial quadrupoles ('Saturn rings'), axial octupoles ('flowers'), linear quadrupoles (poles) and mixed multipole arrangements ('two tone'), which represent just a few examples of the type of structure that can be built using this technique. PMID:19225522

  11. Extended multipole image of a nonideal permanent magnet rotor

    NASA Astrophysics Data System (ADS)

    Kildishev, Alexander V.; Nyenhuis, John A.; Zhilichev, Yuriy N.

    2003-05-01

    Reduction of the external magnetic field (magnetic signature) of large electric motors may be important in military and other applications. This article deals with critical issues in the design and manufacturing of permanent magnet (PM) motors that are responsible for increased magnetic signatures. Emphasis is on analysis of the nonidealities of PM rotors such as imbalances in the permanent magnet excitation system due to manufacturing tolerances and differences in material properties. Spatial harmonic analysis is used to describe the magnetic signature. The rotor simulation considers rectangular PM segments, and uses statistical characterization of possible nonidealities in dimensions, positioning, and magnetization. The approach focuses on lower degree magnetic multipole moments (dipolar, quadrupolar, and octupolar) in spheroidal and spherical domains, and is applied to PM inducing elements.

  12. Active and passive compensation of APPLE II-introduced multipole errors through beam-based measurement

    NASA Astrophysics Data System (ADS)

    Chung, Ting-Yi; Huang, Szu-Jung; Fu, Huang-Wen; Chang, Ho-Ping; Chang, Cheng-Hsiang; Hwang, Ching-Shiang

    2016-08-01

    The effect of an APPLE II-type elliptically polarized undulator (EPU) on the beam dynamics were investigated using active and passive methods. To reduce the tune shift and improve the injection efficiency, dynamic multipole errors were compensated using L-shaped iron shims, which resulted in stable top-up operation for a minimum gap. The skew quadrupole error was compensated using a multipole corrector, which was located downstream of the EPU for minimizing betatron coupling, and it ensured the enhancement of the synchrotron radiation brightness. The investigation methods, a numerical simulation algorithm, a multipole error correction method, and the beam-based measurement results are discussed.

  13. Polarizable Atomic Multipole Solutes in a Poisson-Boltzmann Continuum

    PubMed Central

    Schnieders, Michael J.; Baker, Nathan A.; Ren, Pengyu; Ponder, Jay W.

    2008-01-01

    Modeling the change in the electrostatics of organic molecules upon moving from vacuum into solvent, due to polarization, has long been an interesting problem. In vacuum, experimental values for the dipole moments and polarizabilities of small, rigid molecules are known to high accuracy; however, it has generally been difficult to determine these quantities for a polar molecule in water. A theoretical approach introduced by Onsager used vacuum properties of small molecules, including polarizability, dipole moment and size, to predict experimentally known permittivities of neat liquids via the Poisson equation. Since this important advance in understanding the condensed phase, a large number of computational methods have been developed to study solutes embedded in a continuum via numerical solutions to the Poisson-Boltzmann equation (PBE). Only recently have the classical force fields used for studying biomolecules begun to include explicit polarization in their functional forms. Here we describe the theory underlying a newly developed Polarizable Multipole Poisson-Boltzmann (PMPB) continuum electrostatics model, which builds on the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. As an application of the PMPB methodology, results are presented for several small folded proteins studied by molecular dynamics in explicit water as well as embedded in the PMPB continuum. The dipole moment of each protein increased on average by a factor of 1.27 in explicit water and 1.26 in continuum solvent. The essentially identical electrostatic response in both models suggests that PMPB electrostatics offers an efficient alternative to sampling explicit solvent molecules for a variety of interesting applications, including binding energies, conformational analysis, and pKa prediction. Introduction of 150 mM salt lowered the electrostatic solvation energy between 2–13 kcal/mole, depending on the formal charge of the protein, but had only a

  14. A three-dimensional fast solver for arbitrary vorton distributions

    SciTech Connect

    Strickland, J.H.; Baty, R.S.

    1994-05-01

    A method which is capable of an efficient calculation of the three-dimensional flow field produced by a large system of vortons (discretized regions of vorticity) is presented in this report. The system of vortons can, in turn, be used to model body surfaces, container boundaries, free-surfaces, plumes, jets, and wakes in unsteady three-dimensional flow fields. This method takes advantage of multipole and local series expansions which enables one to make calculations for interactions between groups of vortons which are in well-separated spatial domains rather than having to consider interactions between every pair of vortons. In this work, series expansions for the vector potential of the vorton system are obtained. From such expansions, the three components of velocity can be obtained explicitly. A Fortran computer code FAST3D has been written to calculate the vector potential and the velocity components at selected points in the flow field. In this code, the evaluation points do not have to coincide with the location of the vortons themselves. Test cases have been run to benchmark the truncation errors and CPU time savings associated with the method. Non-dimensional truncation errors for the magnitudes of the vector potential and velocity fields are on the order of 10{sup {minus}4}and 10{sup {minus}3} respectively. Single precision accuracy produces errors in these quantities of up to 10{sup {minus}5}. For less than 1,000 to 2,000 vortons in the field, there is virtually no CPU time savings with the fast solver. For 100,000 vortons in the flow, the fast solver obtains solutions in 1 % to 10% of the time required for the direct solution technique depending upon the configuration.

  15. Fast triangulated vortex methods for the 2D Euler equations

    SciTech Connect

    Russo, G. ); Strain, J.A. )

    1994-04-01

    Vortex methods for inviscid incompressible two-dimensional fluid flow are usually based on blob approximations. This paper presents a vortex method in which the vorticity is approximated by a piecewise polynomial interpolant on a Delaunay triangulation of the vortices. An efficient reconstruction of the Delaunay triangulation at each step makes the method accurate for long times. The vertices of the triangulation move with the fluid velocity, which is reconstructed from the vorticity via a simplified fast multipole method for the Biot-Savart law with a continuous source distribution. The initial distribution of vortices is constructed from the initial vorticity field by an adaptive approximation method which produces good accuracy even for discontinuous initial data. Numerical results show that the method is highly accurate over long time intervals. Experiments with single and multiple circular and elliptical rotating patches of both piecewise constant and smooth vorticity indicate that the method produces much smaller errors than blob methods with the same number of degrees of freedom, at little additional cost. Generalizations to domains with boundaries, viscous flow, and three space dimensions are discussed. 52 refs., 28 figs., 2 tabs.

  16. Fast triangulated vortex methods for the 2D Eulen equations

    NASA Astrophysics Data System (ADS)

    Russo, Giovanni; Strain, John A.

    1994-04-01

    Vortex methods for inviscid incompressible two-dimensional fluid flow are usually based on blob approximations. This paper presents a vortex method in which the vorticity is approximated by a piecewise polynomial interpolant on a Delaunay triangulation of the vortices. An efficient reconstruction of the Delaunay triangulation at each step makes the method accurate for long times. The vertices of the triangulation move with the fluid velocity, which is reconstructed from the vorticity via a simplified fast multipole method for the Biot-Savart law with a continuous source distribution. The initial distribution of vortices is constructed from the initial vorticity field by an adaptive approximation method which produces good accuracy even for discontinuous initial data. Numerical results show that the method is highly accurate over long time intervals. Experiments with single and multiple circular and elliptical rotating patches of both piecewise constant and smooth vorticity indicate that the method produces much smaller errors than blob methods with the same number of degrees of freedom, at little additional cost. Generalizations to domains with boundaries, viscous flow, and three space dimensions are discussed.

  17. Nuclear photonics at ultra-high counting rates and higher multipole excitations

    NASA Astrophysics Data System (ADS)

    Thirolf, P. G.; Habs, D.; Filipescu, D.; Gernhäuser, R.; Günther, M. M.; Jentschel, M.; Marginean, N.; Pietralla, N.

    2012-07-01

    Next-generation γ beams from laser Compton-backscattering facilities like ELI-NP (Bucharest)] or MEGa-Ray (Livermore) will drastically exceed the photon flux presently available at existing facilities, reaching or even exceeding 1013 γ/sec. The beam structure as presently foreseen for MEGa-Ray and ELI-NP builds upon a structure of macro-pulses (˜120 Hz) for the electron beam, accelerated with X-band technology at 11.5 GHz, resulting in a micro structure of 87 ps distance between the electron pulses acting as mirrors for a counterpropagating intense laser. In total each 8.3 ms a γ pulse series with a duration of about 100 ns will impinge on the target, resulting in an instantaneous photon flux of about 1018 γ/s, thus introducing major challenges in view of pile-up. Novel γ optics will be applied to monochromatize the γ beam to ultimately ΔE/E˜10-6. Thus level-selective spectroscopy of higher multipole excitations will become accessible with good contrast for the first time. Fast responding γ detectors, e.g. based on advanced scintillator technology (e.g. LaBr3(Ce)) allow for measurements with count rates as high as 106-107 γ/s without significant drop of performance. Data handling adapted to the beam conditions could be performed by fast digitizing electronics, able to sample data traces during the micro-pulse duration, while the subsequent macro-pulse gap of ca. 8 ms leaves ample time for data readout. A ball of LaBr3 detectors with digital readout appears to best suited for this novel type of nuclear photonics at ultra-high counting rates.

  18. Nuclear photonics at ultra-high counting rates and higher multipole excitations

    SciTech Connect

    Thirolf, P. G.; Habs, D.; Filipescu, D.; Gernhaeuser, R.; Guenther, M. M.; Jentschel, M.; Marginean, N.; Pietralla, N.

    2012-07-09

    Next-generation {gamma} beams from laser Compton-backscattering facilities like ELI-NP (Bucharest)] or MEGa-Ray (Livermore) will drastically exceed the photon flux presently available at existing facilities, reaching or even exceeding 10{sup 13}{gamma}/sec. The beam structure as presently foreseen for MEGa-Ray and ELI-NP builds upon a structure of macro-pulses ({approx}120 Hz) for the electron beam, accelerated with X-band technology at 11.5 GHz, resulting in a micro structure of 87 ps distance between the electron pulses acting as mirrors for a counterpropagating intense laser. In total each 8.3 ms a {gamma} pulse series with a duration of about 100 ns will impinge on the target, resulting in an instantaneous photon flux of about 10{sup 18}{gamma}/s, thus introducing major challenges in view of pile-up. Novel {gamma} optics will be applied to monochromatize the {gamma} beam to ultimately {Delta}E/E{approx}10{sup -6}. Thus level-selective spectroscopy of higher multipole excitations will become accessible with good contrast for the first time. Fast responding {gamma} detectors, e.g. based on advanced scintillator technology (e.g. LaBr{sub 3}(Ce)) allow for measurements with count rates as high as 10{sup 6}-10{sup 7}{gamma}/s without significant drop of performance. Data handling adapted to the beam conditions could be performed by fast digitizing electronics, able to sample data traces during the micro-pulse duration, while the subsequent macro-pulse gap of ca. 8 ms leaves ample time for data readout. A ball of LaBr{sub 3} detectors with digital readout appears to best suited for this novel type of nuclear photonics at ultra-high counting rates.

  19. Constraining halo occupation distribution and cosmic growth rate using multipole power spectrum

    NASA Astrophysics Data System (ADS)

    Hikage, Chiaki

    2014-06-01

    We propose a new method of measuring halo occupation distribution (HOD) together with cosmic growth rate using multipole components of galaxy power spectrum Pl(k). The non-linear redshift-space distortion due to the random motion of satellite galaxies, i.e. Fingers-of-God, generates high-l multipole anisotropy in galaxy clustering, such as the hexadecapole (l = 4) and tetra-hexadecapole (l = 6), which are sensitive to the fraction and the velocity dispersion of satellite galaxies. Using simulated samples following the HOD of luminous red galaxies, we find that the input HOD parameters are successfully reproduced from Pl(k), and that high-l multipole information help to break the degeneracy among HOD parameters. We also show that the measurements of the cosmic growth rate as well as the satellite fraction and velocity dispersions are significantly improved by adding the small-scale information of high-l multipoles.

  20. A fast semi-implicit algorithm for problems of mixed type. [initial-boundary value problems modeled by partial differential equations

    NASA Technical Reports Server (NTRS)

    Frederickson, P. O.; Wessel, W. R.

    1979-01-01

    Certain physical processes are modeled by partial differential equations which are parabolic over part of the domain and elliptic over the remainder. A family of semi-implicit algorithms which are well suited to initial-boundary value problems of this mixed type is discussed. One important feature of these algorithms is the use of an approximate inverse for the solution of the implicit linear system. A strong error analysis results in an estimate of the total error as a function of approximate inverse error e and time step h.

  1. Selected applications of planar permanent magnet multipoles in FEL insertion device design

    SciTech Connect

    Tatchyn, R.

    1993-08-01

    In recent work, a new class of magnetic multipoles based on planar configurations of permanent magnet (PM) material has been developed. These structures, in particular the quadrupole and sextupole, feature fully open horizontal apertures, and are comparable in effectiveness to conventional iron multipole structures. In this paper results of recent measurements of planar PM quadrupoles and sextupoles are reported and selected applications to FEL insertion device design are considered.

  2. A comparison of GPS solutions for strain and SKS fast directions: Implications for modes of shear in the mantle of a plate boundary zone

    NASA Astrophysics Data System (ADS)

    houlie, nicolas; Stern, Tim

    2014-05-01

    We study the strain rate field computed using the GPS GEONET dataset collected during the last decade. We show that we can infer the amount of simple shear accumulated in the mantle by comparing the compression strain orientation with the SKS fast directions. We suggest the mantle beneath the southern part of the south island is under pure shear while to the north the amount of distributed shear is larger. At last, we confirm that, in that context, the strike of New Zealand fault systems make a 60 degree angle with the compression strain rate axis. We compute the strain rate field and the vectors for the principal axis of strain in within New Zealand based on 10 years of data from the Geonet network. A comparison of the principal axis of extension with the fast directions from SKS splitting shows a consistent 20 degree divergence in the northern south Island with the two sets of vectors becoming parallel in central South Island. We firstly interpret these data as confirmation of mantle flow driving crustal kinematics. In addition we suggest the data are consistent with a mode of predominately simple and pure shear in northern and central South Island respectively.

  3. Multipole analysis of unidirectional light scattering from plasmonic dimers

    NASA Astrophysics Data System (ADS)

    Poutrina, E.; Urbas, A.

    2014-11-01

    We analyze unidirectional scattering produced by sub-wavelength plasmonic dimers formed by two silver strips separated by a thin dielectric spacer and embedded in a uniform dielectric medium. Achieving the Kerker condition, which requires matching the strengths of the electric and magnetic-type contributions of the same multipolar order, is possible with such structures for both forward and backward unidirectional scattering by matching the geometric shape-leveraged resonant magnetic dipolar response with the off-resonant electric dipolar contribution. However, unidirectionality is strongly affected by coupling between the two elements in the dimer structure, leading to the manifestation of the electric quadrupole response in the far field. We develop an approach allowing for an easy inverse scattering retrieval of various multipole contributions to the far-field pattern produced by this type of geometry. The retrieval shows unambiguously that the electric quadrupole response contributes up to 30% of the scattered far-field intensity, in addition to strong manifestation of both electric and magnetic dipolar modes. A modified condition for unidirectionality can be developed based on the principle that suppression of radiation in either the forward or backward direction can be achieved whenever the combined strength of multipolar modes of a certain parity, radiating along the propagation direction, matches that of an opposite parity, and noting that parities of electric and magnetic modes interchange with increasing multipole order. With this condition satisfied, unidirectionality of 26 dB/17 dB for forward/backward scattering, respectively, can be achieved with dimer geometries. We also perform a detailed quantitative analysis of scattering cross sections of dimer structures compared to those of Si and gold spheres, accounting for the actual material losses. We show that dimer structures allow for improving backscattering unidirectionality by 10 dB compared to what

  4. Fast and accurate metrology of multi-layered ceramic materials by an automated boundary detection algorithm developed for optical coherence tomography data

    PubMed Central

    Ekberg, Peter; Su, Rong; Chang, Ernest W.; Yun, Seok Hyun; Mattsson, Lars

    2014-01-01

    Optical coherence tomography (OCT) is useful for materials defect analysis and inspection with the additional possibility of quantitative dimensional metrology. Here, we present an automated image-processing algorithm for OCT analysis of roll-to-roll multilayers in 3D manufacturing of advanced ceramics. It has the advantage of avoiding filtering and preset modeling, and will, thus, introduce a simplification. The algorithm is validated for its capability of measuring the thickness of ceramic layers, extracting the boundaries of embedded features with irregular shapes, and detecting the geometric deformations. The accuracy of the algorithm is very high, and the reliability is better than 1 µm when evaluating with the OCT images using the same gauge block step height reference. The method may be suitable for industrial applications to the rapid inspection of manufactured samples with high accuracy and robustness. PMID:24562018

  5. Measurements of diurnal variations and Eddy Covariance (EC) fluxes of glyoxal in the tropical marine boundary layer: description of the Fast LED-CE-DOAS instrument

    NASA Astrophysics Data System (ADS)

    Coburn, S.; Ortega, I.; Thalman, R.; Blomquist, B.; Fairall, C. W.; Volkamer, R.

    2014-06-01

    Here we present first Eddy Covariance (EC) measurements of fluxes of glyoxal, the smallest α-dicarbonyl product of hydrocarbon oxidation, and a precursor for secondary organic aerosol (SOA). The unique physical and chemical properties of glyoxal, i.e., high solubility in water (Henry's Law constant, KH = 4.2 × 105 M atm-1) and short atmospheric lifetime (~2 h at solar noon) make it a unique indicator species for organic carbon oxidation in the marine atmosphere. Previous reports of elevated glyoxal over oceans remain unexplained by atmospheric models. Here we describe a Fast Light Emitting Diode Cavity Enhanced Differential Optical Absorption Spectroscopy (Fast LED-CE-DOAS) instrument to measure diurnal variations and EC fluxes of glyoxal, and inform about its unknown sources. The fast in situ sensor is described, and first results are presented from a cruise deployment over the Eastern tropical Pacific Ocean (20° N to 10° S; 133° W to 85° W) as part of the Tropical Ocean Troposphere Exchange of Reactive Halogens and OVOC (TORERO) field experiment (January to March 2012). The Fast LED-CE-DOAS is a multispectral sensor that selectively and simultaneously measures glyoxal (CHOCHO), nitrogen dioxide (NO2), oxygen dimers (O4) and water vapor (H2O) with ~2 Hz time resolution, and a precision of ~40 pptv Hz-0.5 for glyoxal. The instrument is demonstrated to be a "white-noise" sensor suitable for EC flux measurements; further, highly sensitive and inherently calibrated glyoxal measurements are obtained from temporal averaging of data (~2 pptv detection limit over 1 h). The campaign averaged mixing ratio in the Southern Hemisphere (SH) is found to be 43 ± 9 pptv glyoxal, and is higher than in the Northern Hemisphere (NH: 32 ± 6 pptv; error reflects variability over multiple days). The diurnal variation of glyoxal in the MBL is measured for the first time, and mixing ratios vary by ~8 ppt (NH) and ~12 pptv (SH) over the course of 24 h. Consistently, maxima are

  6. A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains

    NASA Astrophysics Data System (ADS)

    Liska, Sebastian; Colonius, Tim

    2015-11-01

    A novel, parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an infinite staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete operators. The differential algebraic equations describing the temporal evolution of the discrete momentum equation, incompressibility constraint, and the no-slip constraint are numerically solved by combining an integrating factor technique for the viscous term and a half-explicit Runge-Kutta scheme for the convective term. A nested projection that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme. Linear complexity, fast computation rate, and parallel scalability are achieved using recently developed fast multipole methods for difference equations. Results for three-dimensional test problems are presented, and the performance and scaling of the present implementation are discussed.

  7. A multipole superconducting wiggler for Canadian light source

    NASA Astrophysics Data System (ADS)

    Bekhtenev, E. A.; Khruschev, S. V.; Kuper, E. A.; Lev, V. H.; Mezentsev, N. A.; Miginsky, E. G.; Repkov, V. V.; Shkaruba, B. A.; Syrovatin, V. M.; Tsukanov, V. M.

    2006-12-01

    A contract for multipole superconducting wiggler design and fabrication between The University of Saskatchewan and Budker Institute of Nuclear Physics was signed in October 2003. A wiggler with the photons energy range 4 to 40 keV, the maximum field 1.9 T, and the period length as small as possible was required for the micro-XAFS beamline. In 2004 the 2 T 63-pole superconducting wiggler with the average period length 34 mm was fabricated in BINP. To eliminate the undulator-type spectrum, the periodicity of the wiggler was broken. A new approach to the cryostat design enabled long-time (up to 6 months) machine operation without liquid helium refilling (LHe consumption <0.03 l/h). After successful tests the wiggler was installed on the Canadian Light Source (CLS) storage ring with the energy 2.9 GeV in January 2005. The main parameters of the magnet and the cryogenic systems, as well as magnet measurements data, cryogenic system test data, and experimental results during machine operation on the CLS storage ring are presented.

  8. Spectral Kinetic Simulation of the Ideal Multipole Resonance Probe

    NASA Astrophysics Data System (ADS)

    Gong, Junbo; Wilczek, Sebastian; Szeremley, Daniel; Oberrath, Jens; Eremin, Denis; Dobrygin, Wladislaw; Schilling, Christian; Friedrichs, Michael; Brinkmann, Ralf Peter

    2015-09-01

    The term Active Plasma Resonance Spectroscopy (APRS) denotes a class of diagnostic techniques which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency ωpe: An RF signal in the GHz range is coupled into the plasma via an electric probe; the spectral response of the plasma is recorded, and a mathematical model is used to determine plasma parameters such as the electron density ne or the electron temperature Te. One particular realization of the method is the Multipole Resonance Probe (MRP). The ideal MRP is a geometrically simplified version of that probe; it consists of two dielectrically shielded, hemispherical electrodes to which the RF signal is applied. A particle-based numerical algorithm is described which enables a kinetic simulation of the interaction of the probe with the plasma. Similar to the well-known particle-in-cell (PIC), it contains of two modules, a particle pusher and a field solver. The Poisson solver determines, with the help of a truncated expansion into spherical harmonics, the new electric field at each particle position directly without invoking a numerical grid. The effort of the scheme scales linearly with the ensemble size N.

  9. Low pressure characteristics of the multipole resonance probe

    NASA Astrophysics Data System (ADS)

    Brinkmann, Ralf Peter; Oberrath, Jens

    2014-10-01

    The term ``Active plasma resonance spectroscopy'' (APRS) denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency ωpe. The basic idea dates back to the early days of discharge physics but has recently found renewed interest as an approach to industry-compatible plasma diagnostics: A radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded (with the same or another antenna or probe), and a mathematical model is used to determine plasma parameters like the electron density or the electron temperature. When the method is applied to low pressure plasmas (of a few Pa and lower), kinetic effects must be accounted for in the mathematical model. This contribution studies a particular realization of the APRS scheme, the geometrically and electrically symmetric Multipole Resonance Probe (MRP). It is shown that the resonances of the MRP exhibit a residual damping in the limit p --> 0 which cannot be explained by Ohmic dissipation but only by kinetic effects. Supported by the German Federal Ministry of Education and Research (BMBF) in the framework of the PluTO project.

  10. Revised Parameters for the AMOEBA Polarizable Atomic Multipole Water Model.

    PubMed

    Laury, Marie L; Wang, Lee-Ping; Pande, Vijay S; Head-Gordon, Teresa; Ponder, Jay W

    2015-07-23

    A set of improved parameters for the AMOEBA polarizable atomic multipole water model is developed. An automated procedure, ForceBalance, is used to adjust model parameters to enforce agreement with ab initio-derived results for water clusters and experimental data for a variety of liquid phase properties across a broad temperature range. The values reported here for the new AMOEBA14 water model represent a substantial improvement over the previous AMOEBA03 model. The AMOEBA14 model accurately predicts the temperature of maximum density and qualitatively matches the experimental density curve across temperatures from 249 to 373 K. Excellent agreement is observed for the AMOEBA14 model in comparison to experimental properties as a function of temperature, including the second virial coefficient, enthalpy of vaporization, isothermal compressibility, thermal expansion coefficient, and dielectric constant. The viscosity, self-diffusion constant, and surface tension are also well reproduced. In comparison to high-level ab initio results for clusters of 2-20 water molecules, the AMOEBA14 model yields results similar to AMOEBA03 and the direct polarization iAMOEBA models. With advances in computing power, calibration data, and optimization techniques, we recommend the use of the AMOEBA14 water model for future studies employing a polarizable water model. PMID:25683601

  11. Internal conversion coefficients of high multipole transitions: Experiment and theories

    NASA Astrophysics Data System (ADS)

    Gerl, J.; Vijay Sai, K.; Sainath, M.; Gowrishankar, R.; Venkataramaniah, K.

    2008-09-01

    A compilation of the available experimental internal conversion coefficients (ICCs), αT, αK, αL, and ratios K/L and K/LM of high multipole ( L > 2) transitions for a number of elements in the range 21 ⩽ Z ⩽ 94 is presented. Our listing of experimental data includes 194 data sets on 110 E3 transitions, 10 data sets on 6 E4 transitions, 11 data sets on 7 E5 transitions, 38 data sets on 21 M3 transitions, and 132 data sets on 68 M4 transitions. Data with less than 10% experimental uncertainty have been selected for comparison with the theoretical values of Hager and Seltzer [R.S. Hager, E.C. Seltzer, Nucl. Data Tables A 4 (1968) 1], Rosel et al. [F. Rösel, H.M. Fries, K. Alder, H.C. Pauli, At. Data Nucl. Data Tables 21 (1978) 91], and BRICC. The relative percentage deviations (%Δ) have been calculated for each of the above theories and the averages (%Δ¯) are estimated. The Band et al. [I.M. Band, M.B. Trzhaskovskaya, C.W. Nestor Jr., P.O. Tikkanen, S. Raman, At. Data Nucl. Data Tables 81 (2002) 1] tables, using the BRICC interpolation code, are seen to give theoretical ICCs closest to experimental values.

  12. Beamline 10: A multipole wiggler beamline at SSRL

    SciTech Connect

    Karpenko, V.; Kinney, J. H.; Kulkarni, S.; Neufeld, K.; Poppe, C.; Tirsell, K. G.; Wong, J.; Cerino, J.; Troxel, T.; Yang, J.; and others

    1989-07-01

    A beamline has been constructed at Stanford Synchrotron Radiation Laboratory (SSRL) whose radiation source is a multipole permanent magnet wiggler installed in a straight section of the SPEAR 3--3.5 GeV electron storage ring. The wiggler is a hybrid design that utilizes Nd--Fe alloy magnet material combined with Vanadium Permendur poles. It is approximately 2 m long and has 15 full wiggler periods. Its field is regulated by varying its gap height. It has a peak operating field, limited by the electron beam vacuum chamber vertical aperture, of 1.4 T. The beamline consists of vacuum, safety, and optical components capable of transporting photons to one hard x-ray (3--30 keV) end station, with provisions for implementing up to two additional branch lines. The existing hard x-ray branch can be focused by a Pt-coated toroidal mirror with a cutoff energy of approximately 22 keV. The experimental end station is serviced by a Hower--Brown type double crystal monochromator. The wiggler and beamline construction was completed in the fall of 1987 and was operated for a brief period for characterization and experimental use. We present design details and results of the initial characterization studies.

  13. Beamline 10: A multipole wiggler beamline at SSRL (invited)

    NASA Astrophysics Data System (ADS)

    Karpenko, V.; Kinney, J. H.; Kulkarni, S.; Neufeld, K.; Poppe, C.; Tirsell, K. G.; Wong, J.; Cerino, J.; Troxel, T.; Yang, J.; Hoyer, E.; Green, M.; Humphries, D.; Marks, S.; Plate, D.

    1989-07-01

    A beamline has been constructed at Stanford Synchrotron Radiation Laboratory (SSRL) whose radiation source is a multipole permanent magnet wiggler installed in a straight section of the SPEAR 3-3.5 GeV electron storage ring. The wiggler is a hybrid design that utilizes Nd-Fe alloy magnet material combined with Vanadium Permendur poles. It is approximately 2 m long and has 15 full wiggler periods. Its field is regulated by varying its gap height. It has a peak operating field, limited by the electron beam vacuum chamber vertical aperture, of 1.4 T. The beamline consists of vacuum, safety, and optical components capable of transporting photons to one hard x-ray (3-30 keV) end station, with provisions for implementing up to two additional branch lines. The existing hard x-ray branch can be focused by a Pt-coated toroidal mirror with a cutoff energy of approximately 22 keV. The experimental end station is serviced by a Hower-Brown type double crystal monochromator. The wiggler and beamline construction was completed in the fall of 1987 and was operated for a brief period for characterization and experimental use. We present design details and results of the initial characterization studies.

  14. RKKY Interactions between Multipole Moments in URu2Si2

    NASA Astrophysics Data System (ADS)

    Hanzawa, Katsurou

    2015-02-01

    We evaluate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between multipole moments of U4+ ions with 5f2 configuration responsible for the hidden order in URu2Si2. We adopt a generalized periodic Anderson model taking account of all relevant on-site couplings in the 5f2 state and a practical conduction-band structure. A tight-binding model is constructed in terms of maximally localized Wannier functions for conduction bands calculated by a band calculation for ThRu2Si2, and c-f hybridizations are represented by the Slater-Koster integrals. For the Γ1-Γ5 (singlet-doublet) crystalline-electric-field level scheme for 5f2, we obtain the RRKY interactions composed of a predominant antiferro (AF) octupole interaction of Eu (x(y2 - z2),y(z2 - x2)) symmetry, an AF dipole interaction of A2u (z), and a ferro quadrupole interaction of B1g (x2 - y2). Relevance of the present results to the properties of URu2Si2 are discussed. The present formulae can apply to the estimation of c-f exchange and RKKY interactions for rare-earth and actinide heavy-fermion compounds with general fn configurations.

  15. Neptune radio emission in dipole and multipole magnetic fields

    NASA Technical Reports Server (NTRS)

    Sawyer, C. B.; King, N. V.; Romig, J. H.; Warwick, J. W.

    1995-01-01

    We study Neptune's smooth radio emission in two ways: we simulate the observations and we then consider the radio effects of Neptune's magnetic multipoles. A procedure to deduce the characteristics of radio sources observed by the Planetary Radio Astronomy experiment minimizes limiting assumptions and maximizes use of the data, including quantitative measurement of circular polarization. Study of specific sources simulates time variation of intensity and apparent polarization of their integrated emission over an extended time period. The method is applied to Neptune smooth recurrent emission (SRE). Time series are modeled with both broad and beamed emission patterns, and at two frequencies which exhibit different time variation of polarization. These dipole-based results are overturned by consideration of more complex models of Neptune's magnetic field. Any smooth emission from the anticipated auroral radio source is weak and briefly observed. Dominant SRE originates complex fields at midlatitude. Possible SRE source locations overlap that of 'high-latitude' emission (HLE) between +(out) and -(in) quadrupoles. This is the first identification of multipolar magnetic structure with a major source of planetary radio emission.

  16. Boundary-corrected four-body continuum-intermediate-state method: Single-electron capture from heliumlike atomic systems by fast nuclei

    NASA Astrophysics Data System (ADS)

    Mančev, Ivan; Milojević, Nenad; Belkić, Dževad

    2015-06-01

    Single charge exchange in collisions between bare projectiles and heliumlike atomic systems at intermediate and high incident energies is examined by using the four-body formalism of the first- and second-order theories. The main purpose of the present study is to investigate the relative importance of the intermediate ionization continua of the captured electron compared to the usual direct path of the single electron transfer from a target to a projectile. In order to achieve this goal, comprehensive comparisons are made between the four-body boundary-corrected continuum-intermediate-states (BCIS-4B) method and the four-body boundary-corrected first Born (CB1-4B) method. The perturbation potential is the same in the CB1-4B and BCIS-4B methods. Both methods satisfy the correct boundary conditions in the entrance and exit channels. However, unlike the CB1-4B method, the second-order BCIS-4B method takes into account the electronic Coulomb continuum-intermediate states in either the entrance or the exit channel depending on whether the post or the prior version of the transition amplitude is used. Hence, by comparing the results from these two theories, the relative importance of the intermediate ionization electronic continua can be assessed within the four-body formalism of scattering theory. The BCIS-4B method predicts the usual second-order effect through double scattering of the captured electron on two nuclei as a quantum-mechanical counterpart of the Thomas classical two-step, billiard-type collision. The physical mechanism for this effect in the BCIS-4B method is also comprised of two steps such that ionization occurs first. This is followed by capture of the electron by the projectile with both processes taking place on the energy shell. Moreover, the role of the second, noncaptured electron in a heliumlike target is revisited. To this end, the BCIS-4B method describes the effect of capture of one electron by the interaction of the projectile nucleus with

  17. Fast Poisson, Fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds

    SciTech Connect

    Wiegmann, A.

    1999-06-01

    FFT-based fast Poisson and fast Helmholtz solvers on rectangular parallelepipeds for periodic boundary conditions in one-, two and three space dimensions can also be used to solve Dirichlet and Neumann boundary value problems. For non-zero boundary conditions, this is the special, grid-aligned case of jump corrections used in the Explicit Jump Immersed Interface method. Fast elastostatic solvers for periodic boundary conditions in two and three dimensions can also be based on the FFT. From the periodic solvers we derive fast solvers for the new 'normal' boundary conditions and essential boundary conditions on rectangular parallelepipeds. The periodic case allows a simple proof of existence and uniqueness of the solutions to the discretization of normal boundary conditions. Numerical examples demonstrate the efficiency of the fast elastostatic solvers for non-periodic boundary conditions. More importantly, the fast solvers on rectangular parallelepipeds can be used together with the Immersed Interface Method to solve problems on non-rectangular domains with general boundary conditions. Details of this are reported in the preprint The Explicit Jump Immersed Interface Method for 2D Linear Elastostatics by the author.

  18. The Importance of Using Explicit and then Implicit Schemes in the Fast time-scale Rupturing at Oceanic-Continental Boundary

    NASA Astrophysics Data System (ADS)

    So, B.; Yuen, D. A.; Lee, S.

    2011-12-01

    Numerical modeling in geodynamics, such as subduction and lithospheric rupture, normally uses only one scheme (e.g., implicit or explicit). However every geodynamical phenomena has a multi-time-scale instability. So these problems cannot be solved completely by just one numerical scheme since implicit and explicit schemes have different characteristics and stabilize in different time step size. That's why modelers should select an appropriate scheme for their problems. In our fully coupled thermal-mechanical finite element modeling for asymmetric instability initiation induced by shear modulus contrast between oceanic and continental lithospheres, two simply attached lithospheres with different shear modulus but having same visco-plastic rheologies are compressed with constant velocity of few centimeters per year. We use both explicit and implicit schemes at stages of elastic energy release and strengthening of shear localization, respectively. Since elastic energy quickly propagates from top and bottom of lithosphere (>1500 km/Myr), the employment of explicit scheme is more suitable to understand thermal runaway effect than implicit scheme at the initial stage of stored elastic energy release (i.e., this stage needs small time step size). The calculation results with only-implicit scheme and explicit-implicit hybrid scheme are different, because the latter can calculate fast time-scale energy dissipation and temperature field better than the former. The small temperature difference between implicit and explicit schemes may cause the large difference at later stage due to thermal-mechanical feedback. To investigate the timing of the initiation of asymmetric instability crossing the interface, temperature and plastic energy distributions are calculated on fine grid composed of shear modulus contrast and activation energy for a period of 1 Myr. We found that asymmetric shear instabilities are induced by a elastic shear modulus contrast over an wide range of

  19. PACER -- A fast running computer code for the calculation of short-term containment/confinement loads following coolant boundary failure. Volume 2: User information

    SciTech Connect

    Sienicki, J.J.

    1997-06-01

    A fast running and simple computer code has been developed to calculate pressure loadings inside light water reactor containments/confinements under loss-of-coolant accident conditions. PACER was originally developed to calculate containment/confinement pressure and temperature time histories for loss-of-coolant accidents in Soviet-designed VVER reactors and is relevant to the activities of the US International Nuclear Safety Center. The code employs a multicompartment representation of the containment volume and is focused upon application to early time containment phenomena during and immediately following blowdown. PACER has been developed for FORTRAN 77 and earlier versions of FORTRAN. The code has been successfully compiled and executed on SUN SPARC and Hewlett-Packard HP-735 workstations provided that appropriate compiler options are specified. The code incorporates both capabilities built around a hardwired default generic VVER-440 Model V230 design as well as fairly general user-defined input. However, array dimensions are hardwired and must be changed by modifying the source code if the number of compartments/cells differs from the default number of nine. Detailed input instructions are provided as well as a description of outputs. Input files and selected output are presented for two sample problems run on both HP-735 and SUN SPARC workstations.

  20. Efficient Kriging via Fast Matrix-Vector Products

    NASA Technical Reports Server (NTRS)

    Memarsadeghi, Nargess; Raykar, Vikas C.; Duraiswami, Ramani; Mount, David M.

    2008-01-01

    Interpolating scattered data points is a problem of wide ranging interest. Ordinary kriging is an optimal scattered data estimator, widely used in geosciences and remote sensing. A generalized version of this technique, called cokriging, can be used for image fusion of remotely sensed data. However, it is computationally very expensive for large data sets. We demonstrate the time efficiency and accuracy of approximating ordinary kriging through the use of fast matrixvector products combined with iterative methods. We used methods based on the fast Multipole methods and nearest neighbor searching techniques for implementations of the fast matrix-vector products.

  1. Boundary Crossing and Boundary Objects

    ERIC Educational Resources Information Center

    Akkerman, Sanne F.; Bakker, Arthur

    2011-01-01

    Diversity and mobility in education and work present a paramount challenge that needs better conceptualization in educational theory. This challenge has been addressed by educational scholars with the notion of "boundaries", particularly by the concepts of "boundary crossing" and "boundary objects". Although studies on boundary crossing and…

  2. a Detailed Proof of the Fundamental Theorem of STF Multipole Expansion in Linearized Gravity

    NASA Astrophysics Data System (ADS)

    Zschocke, Sven

    2014-10-01

    The linearized field equations of general relativity in harmonic coordinates are given by an inhomogeneous wave equation. In the region exterior to the matter field, the retarded solution of this wave equation can be expanded in terms of 10 Cartesian symmetric and tracefree (STF) multipoles in post-Minkowskian approximation. For such a multipole decomposition only three and rather weak assumptions are required: (1) No-incoming-radiation condition. (2) The matter source is spatially compact. (3) A spherical expansion for the metric outside the matter source is possible. During the last decades, the STF multipole expansion has been established as a powerful tool in several fields of gravitational physics: celestial mechanics, theory of gravitational waves and in the theory of light propagation and astrometry. But despite its formidable importance, an explicit proof of the fundamental theorem of STF multipole expansion has not been presented so far, while only some parts of it are distributed into several publications. In a technical but more didactical form, an explicit and detailed mathematical proof of each individual step of this important theorem of STF multipole expansion is represented.

  3. a Detailed Proof of the Fundamental Theorem of STF Multipole Expansion in Linearized Gravity

    NASA Astrophysics Data System (ADS)

    Zschocke, Sven

    2013-07-01

    The linearized field equations of general relativity in harmonic coordinates are given by an inhomogeneous wave equation. In the region exterior to the matter field, the retarded solution of this wave equation can be expanded in terms of 10 Cartesian symmetric and tracefree (STF) multipoles in post-Minkowskian approximation. For such a multipole decomposition only three and rather weak assumptions are required: (1) No-incoming-radiation condition. (2) The matter source is spatially compact. (3) A spherical expansion for the metric outside the matter source is possible. During the last decades, the STF multipole expansion has been established as a powerful tool in several fields of gravitational physics: celestial mechanics, theory of gravitational waves and in the theory of light propagation and astrometry. But despite its formidable importance, an explicit proof of the fundamental theorem of STF multipole expansion has not been presented so far, while only some parts of it are distributed into several publications. In a technical but more didactical form, an explicit and detailed mathematical proof of each individual step of this important theorem of STF multipole expansion is represented.

  4. United polarizable multipole water model for molecular mechanics simulation.

    PubMed

    Qi, Rui; Wang, Lee-Ping; Wang, Qiantao; Pande, Vijay S; Ren, Pengyu

    2015-07-01

    We report the development of a united AMOEBA (uAMOEBA) polarizable water model, which is computationally 3-5 times more efficient than the three-site AMOEBA03 model in molecular dynamics simulations while providing comparable accuracy for gas-phase and liquid properties. In this coarse-grained polarizable water model, both electrostatic (permanent and induced) and van der Waals representations have been reduced to a single site located at the oxygen atom. The permanent charge distribution is described via the molecular dipole and quadrupole moments and the many-body polarization via an isotropic molecular polarizability, all located at the oxygen center. Similarly, a single van der Waals interaction site is used for each water molecule. Hydrogen atoms are retained only for the purpose of defining local frames for the molecular multipole moments and intramolecular vibrational modes. The parameters have been derived based on a combination of ab initio quantum mechanical and experimental data set containing gas-phase cluster structures and energies, and liquid thermodynamic properties. For validation, additional properties including dimer interaction energy, liquid structures, self-diffusion coefficient, and shear viscosity have been evaluated. The results demonstrate good transferability from the gas to the liquid phase over a wide range of temperatures, and from nonpolar to polar environments, due to the presence of molecular polarizability. The water coordination, hydrogen-bonding structure, and dynamic properties given by uAMOEBA are similar to those derived from the all-atom AMOEBA03 model and experiments. Thus, the current model is an accurate and efficient alternative for modeling water. PMID:26156485

  5. United polarizable multipole water model for molecular mechanics simulation

    NASA Astrophysics Data System (ADS)

    Qi, Rui; Wang, Lee-Ping; Wang, Qiantao; Pande, Vijay S.; Ren, Pengyu

    2015-07-01

    We report the development of a united AMOEBA (uAMOEBA) polarizable water model, which is computationally 3-5 times more efficient than the three-site AMOEBA03 model in molecular dynamics simulations while providing comparable accuracy for gas-phase and liquid properties. In this coarse-grained polarizable water model, both electrostatic (permanent and induced) and van der Waals representations have been reduced to a single site located at the oxygen atom. The permanent charge distribution is described via the molecular dipole and quadrupole moments and the many-body polarization via an isotropic molecular polarizability, all located at the oxygen center. Similarly, a single van der Waals interaction site is used for each water molecule. Hydrogen atoms are retained only for the purpose of defining local frames for the molecular multipole moments and intramolecular vibrational modes. The parameters have been derived based on a combination of ab initio quantum mechanical and experimental data set containing gas-phase cluster structures and energies, and liquid thermodynamic properties. For validation, additional properties including dimer interaction energy, liquid structures, self-diffusion coefficient, and shear viscosity have been evaluated. The results demonstrate good transferability from the gas to the liquid phase over a wide range of temperatures, and from nonpolar to polar environments, due to the presence of molecular polarizability. The water coordination, hydrogen-bonding structure, and dynamic properties given by uAMOEBA are similar to those derived from the all-atom AMOEBA03 model and experiments. Thus, the current model is an accurate and efficient alternative for modeling water.

  6. United polarizable multipole water model for molecular mechanics simulation

    SciTech Connect

    Qi, Rui; Wang, Qiantao; Ren, Pengyu; Wang, Lee-Ping; Pande, Vijay S.

    2015-07-07

    We report the development of a united AMOEBA (uAMOEBA) polarizable water model, which is computationally 3–5 times more efficient than the three-site AMOEBA03 model in molecular dynamics simulations while providing comparable accuracy for gas-phase and liquid properties. In this coarse-grained polarizable water model, both electrostatic (permanent and induced) and van der Waals representations have been reduced to a single site located at the oxygen atom. The permanent charge distribution is described via the molecular dipole and quadrupole moments and the many-body polarization via an isotropic molecular polarizability, all located at the oxygen center. Similarly, a single van der Waals interaction site is used for each water molecule. Hydrogen atoms are retained only for the purpose of defining local frames for the molecular multipole moments and intramolecular vibrational modes. The parameters have been derived based on a combination of ab initio quantum mechanical and experimental data set containing gas-phase cluster structures and energies, and liquid thermodynamic properties. For validation, additional properties including dimer interaction energy, liquid structures, self-diffusion coefficient, and shear viscosity have been evaluated. The results demonstrate good transferability from the gas to the liquid phase over a wide range of temperatures, and from nonpolar to polar environments, due to the presence of molecular polarizability. The water coordination, hydrogen-bonding structure, and dynamic properties given by uAMOEBA are similar to those derived from the all-atom AMOEBA03 model and experiments. Thus, the current model is an accurate and efficient alternative for modeling water.

  7. United polarizable multipole water model for molecular mechanics simulation

    PubMed Central

    Qi, Rui; Wang, Lee-Ping; Wang, Qiantao; Pande, Vijay S.; Ren, Pengyu

    2015-01-01

    We report the development of a united AMOEBA (uAMOEBA) polarizable water model, which is computationally 3–5 times more efficient than the three-site AMOEBA03 model in molecular dynamics simulations while providing comparable accuracy for gas-phase and liquid properties. In this coarse-grained polarizable water model, both electrostatic (permanent and induced) and van der Waals representations have been reduced to a single site located at the oxygen atom. The permanent charge distribution is described via the molecular dipole and quadrupole moments and the many-body polarization via an isotropic molecular polarizability, all located at the oxygen center. Similarly, a single van der Waals interaction site is used for each water molecule. Hydrogen atoms are retained only for the purpose of defining local frames for the molecular multipole moments and intramolecular vibrational modes. The parameters have been derived based on a combination of ab initio quantum mechanical and experimental data set containing gas-phase cluster structures and energies, and liquid thermodynamic properties. For validation, additional properties including dimer interaction energy, liquid structures, self-diffusion coefficient, and shear viscosity have been evaluated. The results demonstrate good transferability from the gas to the liquid phase over a wide range of temperatures, and from nonpolar to polar environments, due to the presence of molecular polarizability. The water coordination, hydrogen-bonding structure, and dynamic properties given by uAMOEBA are similar to those derived from the all-atom AMOEBA03 model and experiments. Thus, the current model is an accurate and efficient alternative for modeling water. PMID:26156485

  8. Multipole correction of atomic monopole models of molecular charge distribution. I. Peptides

    NASA Technical Reports Server (NTRS)

    Sokalski, W. A.; Keller, D. A.; Ornstein, R. L.; Rein, R.

    1993-01-01

    The defects in atomic monopole models of molecular charge distribution have been analyzed for several model-blocked peptides and compared with accurate quantum chemical values. The results indicate that the angular characteristics of the molecular electrostatic potential around functional groups capable of forming hydrogen bonds can be considerably distorted within various models relying upon isotropic atomic charges only. It is shown that these defects can be corrected by augmenting the atomic point charge models by cumulative atomic multipole moments (CAMMs). Alternatively, sets of off-center atomic point charges could be automatically derived from respective multipoles, providing approximately equivalent corrections. For the first time, correlated atomic multipoles have been calculated for N-acetyl, N'-methylamide-blocked derivatives of glycine, alanine, cysteine, threonine, leucine, lysine, and serine using the MP2 method. The role of the correlation effects in the peptide molecular charge distribution are discussed.

  9. The electrostatic potential generated by topological atoms. II. Inverse multipole moments.

    PubMed

    Rafat, M; Popelier, P L A

    2005-11-22

    Quantum chemical topology defines finite atoms, whose bounded electron density generates a well-defined electrostatic potential. A multipole expansion based on spherical tensors provides a potential that is formally convergent outside the divergence sphere. Part I of this series [P. L. A. Popelier and M. Rafat, Chem. Phys. Lett.376, 148 (2003)] showed that a continuous multipole expansion expands the convergence region, thereby allowing the electrostatic potential to be evaluated at short range. Here, we propose a different method, based on "inverse" multipole moments, enabling an expansion that converges everywhere. These moments are defined by inverse (i.e., negative) powers of the magnitude of the position vector describing the electron density inside the atom. We illustrate this technique on nitrogen in N(2), oxygen in H(2)O, and oxygen in the phenolic group of the amino acid tyrosine. The proposed method constitutes a considerable advance over the method presented in Part I. PMID:16351236

  10. Global Aspects of Charged Particle Motion in Axially Symmetric Multipole Magnetic Fields

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    2003-01-01

    The motion of a single charged particle in the space outside of a compact region of steady currents is investigated. The charged particle is assumed to produce negligible electromagnetic radiation, so that its energy is conserved. The source of the magnetic field is represented as a point multipole. After a general description, attention is focused on magnetic fields with axial symmetry. Lagrangian dynamical theory is utilized to identify constants of the motion as well as the equations of motion themselves. The qualitative method of Stonner is used to examine charged particle motion in axisymmetric multipole fields of all orders. Although the equations of motion generally have no analytical solutions and must be integrated numerically to produce a specific orbit, a topological examination of dynamics is possible, and can be used, d la Stonner, to completely describe the global aspects of the motion of a single charged particle in a space with an axisymmetric multipole magnetic field.

  11. A convergent multipole expansion for 1,3 and 1,4 Coulomb interactions

    NASA Astrophysics Data System (ADS)

    Rafat, M.; Popelier, P. L. A.

    2006-04-01

    Traditionally force fields express 1,3 and 1,4 interactions as bonded terms via potentials that involve valence and torsion angles, respectively. These interactions are not modeled by point charge terms, which are confined to electrostatic interactions between more distant atoms (1,n where n >4). Here we show that both 1,3 and 1,4 interactions can be described on the same footing as 1,n (n>4) interactions by a convergent multipole expansion of the Coulomb energy of the participating atom pairs. The atomic multipole moments are generated by the theory of quantum chemical topology. The procedure to make the multipole expansion convergent is based on a "shift procedure" described in earlier work [L. Joubert and P. L. A. Popelier, Molec. Phys. 100, 3357 (2002)].

  12. Tunable multipole resonances in plasmonic crystals made by four-beam holographic lithography

    NASA Astrophysics Data System (ADS)

    Luo, Y.; Li, X.; Zhang, X.; Prybolsky, S.; Shepard, G. D.; Strauf, S.

    2016-02-01

    Plasmonic nanostructures confine light to sub-wavelength scales, resulting in drastically enhanced light-matter interactions. Recent interest has focused on controlled symmetry breaking to create higher-order multipole plasmonic modes that store electromagnetic energy more efficiently than dipole modes. Here we demonstrate that four-beam holographic lithography enables fabrication of large-area plasmonic crystals with near-field coupled plasmons as well as deliberately broken symmetry to sustain multipole modes and Fano-resonances. Compared with the spectrally broad dipole modes we demonstrate an order of magnitude improved Q-factors (Q = 21) when the quadrupole mode is activated. We further demonstrate continuous tuning of the Fano-resonances using the polarization state of the incident light beam. The demonstrated technique opens possibilities to extend the rich physics of multipole plasmonic modes to wafer-scale applications that demand low-cost and high-throughput.

  13. Development of a Transient Acoustic Boundary Element Method to Predict the Noise Signature of Swimming Fish

    NASA Astrophysics Data System (ADS)

    Wagenhoffer, Nathan; Moored, Keith; Jaworski, Justin

    2015-11-01

    Animals have evolved flexible wings and fins to efficiently and quietly propel themselves through the air and water. The design of quiet and efficient bio-inspired propulsive concepts requires a rapid, unified computational framework that integrates three essential features: the fluid mechanics, the elastic structural response, and the noise generation. This study focuses on the development, validation, and demonstration of a transient, two-dimensional acoustic boundary element solver accelerated by a fast multipole algorithm. The resulting acoustic solver is used to characterize the acoustic signature produced by a vortex street advecting over a NACA 0012 airfoil, which is representative of vortex-body interactions that occur in schools of swimming fish. Both 2S and 2P canonical vortex streets generated by fish are investigated over the range of Strouhal number 0 . 2 < St < 0 . 4 , and the acoustic signature of the airfoil is quantified. This study provides the first estimate of the noise signature of a school of swimming fish. Lehigh University CORE Grant.

  14. Quantum Phase for an Electric Multipole Moment in Noncommutative Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Hekim, Mamatabdulla; Anwar, Abduwali; Wang, Jianhua

    2016-02-01

    We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric multipole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations, we obtain quantum phases of the electric multipole moment both on a noncommutative space and a noncommutative phase space. We demonstrate that these phase are geometric and dispersive.

  15. On the stability of two-layer geostrophic point-vortex multipoles

    NASA Astrophysics Data System (ADS)

    Kizner, Ziv

    2014-04-01

    A point-vortex multipole is an ensemble of m+1 vortices (m = 2, 3, …) possessing a m-fold symmetry, with the "core vortex" being located at the centre and m identical "satellite vortices" located at the vertices of an equilateral m-sided polygon (at m > 2) or at the ends of a straight-line segment (at m = 2). At m = 2, m = 3, and m = 4, the multipole is commonly termed a tripole, a quadrupole, and a pentapole, respectively, and the distance from the core vortex to the satellite vortices, the multipole leg. A multipole is said to be stable if, in response to sufficiently small initial perturbations in the distances between the vortices, the variations in the distances remain small for all times. The main issue of this article is an analytical study of the nonlinear stability of point-vortex tripoles characterized by that their core and satellite vortices reside in different layers of a two-layer f-plane quasigeostrophic model. Also the stability of pentapoles and quadrupoles is discussed. The parameters affecting the stability properties of a multipole are the length of its leg and the intensity of the core vortex relative to the satellite vortices. Among the invariants of the dynamical system that describes the motion of an ensemble of m+1 vortices, there are two ones depending on the distances between the vortices only. To establish the stability/instability of a multipole, we consider the restriction of one of the two invariants to the sheet (in the phase space) constituted by the states at which the second invariant takes the same value as at the multipole equilibrium state. Two versions of the method are presented and employed to analyze the stability of collinear states (m = 2) and non-collinear states (m > 2). For tripoles, complete stability analysis is performed resulting in the determination of the regions of stability/instability in the parameter plane. Depending on the parameters, a multipole can rotate clockwise or counterclockwise, and also can be

  16. Multipole Field Effects for the Superconducting Parallel-Bar Deflecting/Crabbing Cavities

    SciTech Connect

    De Silva, Payagalage Subashini Uddika; Delayen, Jean Roger

    2012-09-01

    The superconducting parallel-bar deflecting/crabbing cavity is currently being considered as one of the design options in rf separation for the Jefferson Lab 12 GeV upgrade and for the crabbing cavity for the proposed LHC luminosity upgrade. Knowledge of multipole field effects is important for accurate beam dynamics study of rf structures. The multipole components can be accurately determined numerically using the electromagnetic surface field data in the rf structure. This paper discusses the detailed analysis of those components for the fundamental deflecting/crabbing mode and higher order modes in the parallel-bar deflecting/crabbing cavity.

  17. Apparatus and method of dissociating ions in a multipole ion guide

    DOEpatents

    Webb, Ian K.; Tang, Keqi; Smith, Richard D.; Ibrahim, Yehia M.; Anderson, Gordon A.

    2014-07-08

    A method of dissociating ions in a multipole ion guide is disclosed. A stream of charged ions is supplied to the ion guide. A main RF field is applied to the ion guide to confine the ions through the ion guide. An excitation RF field is applied to one pair of rods of the ion guide. The ions undergo dissociation when the applied excitation RF field is resonant with a secular frequency of the ions. The multipole ion guide is, but not limited to, a quadrupole, a hexapole, and an octopole.

  18. Quantum Phase for an Electric Multipole Moment in Noncommutative Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Hekim, Mamatabdulla; Anwar, Abduwali; Wang, Jianhua

    2016-07-01

    We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric multipole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations, we obtain quantum phases of the electric multipole moment both on a noncommutative space and a noncommutative phase space. We demonstrate that these phase are geometric and dispersive.

  19. Effects of Crab Cavities' Multipole Content in an Electron-Ion Collider

    SciTech Connect

    Satogata, Todd J.; Morozov, Vasiliy; Delayen, Jean R.; Castillo, Alejandro

    2015-09-01

    The impact on the beam dynamics of the Medium Energy Electron-Ion Colider (MEIC) due to the multipole content of the 750 MHz crab cavity was studied using thin multipole elements for 6D phase space particle tracking in ELEGANT. Target values of the sextupole component for the cavity’s field expansion were used to perform preliminary studies on the proton beam stability when compared to the case of pure dipole content of the rf kicks. Finally, important effects on the beam sizes due to non-linear components of the crab cavities’ fields were identified, and some criteria for their future study were proposed.

  20. PARAMETRIC TENSION BETWEEN EVEN AND ODD MULTIPOLE DATA OF THE WMAP POWER SPECTRUM: UNACCOUNTED CONTAMINATION OR MISSING PARAMETERS?

    SciTech Connect

    Kim, Jaiseung; Naselsky, Pavel

    2010-12-01

    There exists power contrast in even and odd multipoles of the WMAP power spectrum at low and intermediate multipole ranges. This anomaly is explicitly associated with the angular power spectrum, which is heavily used for cosmological model fitting. Having noted this, we have investigated whether even (odd) multipole data set is individually consistent with the WMAP concordance model. Our investigation shows that the WMAP concordance model does not make a good fit for even (odd) multipole data set, which indicates parametric tension between even and odd multipole data set. Noting that tension is highest in primordial power spectrum parameters, we have additionally considered a running spectral index, but found that tension increases to even a higher level. We believe these parametric tensions may be indications of unaccounted contamination or imperfection of the model.

  1. Higher-order multipole amplitudes in charmonium radiative transitions

    NASA Astrophysics Data System (ADS)

    Artuso, M.; Blusk, S.; Khalil, S.; Mountain, R.; Randrianarivony, K.; Skwarnicki, T.; Stone, S.; Wang, J. C.; Zhang, L. M.; Bonvicini, G.; Cinabro, D.; Lincoln, A.; Smith, M. J.; Zhou, P.; Zhu, J.; Naik, P.; Rademacker, J.; Asner, D. M.; Edwards, K. W.; Reed, J.; Robichaud, A. N.; Tatishvili, G.; White, E. J.; Briere, R. A.; Vogel, H.; Onyisi, P. U. E.; Rosner, J. L.; Alexander, J. P.; Cassel, D. G.; Ehrlich, R.; Fields, L.; Galik, R. S.; Gibbons, L.; Gray, S. W.; Hartill, D. L.; Heltsley, B. K.; Hunt, J. M.; Kreinick, D. L.; Kuznetsov, V. E.; Ledoux, J.; Mahlke-Krüger, H.; Patterson, J. R.; Peterson, D.; Riley, D.; Ryd, A.; Sadoff, A. J.; Shi, X.; Stroiney, S.; Sun, W. M.; Yelton, J.; Rubin, P.; Lowrey, N.; Mehrabyan, S.; Selen, M.; Wiss, J.; Kornicer, M.; Mitchell, R. E.; Shepherd, M. R.; Tarbert, C. M.; Besson, D.; Pedlar, T. K.; Xavier, J.; Cronin-Hennessy, D.; Gao, K. Y.; Hietala, J.; Poling, R.; Zweber, P.; Dobbs, S.; Metreveli, Z.; Seth, K. K.; Tan, B. J. Y.; Tomaradze, A.; Brisbane, S.; Libby, J.; Martin, L.; Powell, A.; Spradlin, P.; Thomas, C.; Wilkinson, G.; Mendez, H.; Ge, J. Y.; Miller, D. H.; Shipsey, I. P. J.; Xin, B.; Adams, G. S.; Hu, D.; Moziak, B.; Napolitano, J.; Ecklund, K. M.; Insler, J.; Muramatsu, H.; Park, C. S.; Thorndike, E. H.; Yang, F.

    2009-12-01

    Using 24×106 ψ'≡ψ(2S) decays in CLEO-c, we have searched for higher multipole admixtures in electric-dipole-dominated radiative transitions in charmonia. We find good agreement between our data and theoretical predictions for magnetic quadrupole (M2) amplitudes in the transitions ψ'→γχc1,c2 and χc1,c2→γJ/ψ, in striking contrast to some previous measurements. Let b2J and a2J denote the normalized M2 amplitudes in the respective aforementioned decays, where the superscript J refers to the angular momentum of the χcJ. By performing unbinned maximum likelihood fits to full five-parameter angular distributions, we found the following values of M2 admixtures for Jχ=1: a2J=1=(-6.26±0.63±0.24)×10-2 and b2J=1=(2.76±0.73±0.23)×10-2, which agree well with theoretical expectations for a vanishing anomalous magnetic moment of the charm quark. For Jχ=2, if we fix the electric octupole (E3) amplitudes to zero as theory predicts for transitions between charmonium S states and P states, we find a2J=2=(-9.3±1.6±0.3)×10-2 and b2J=2=(1.0±1.3±0.3)×10-2. If we allow for E3 amplitudes we find, with a four-parameter fit, a2J=2=(-7.9±1.9±0.3)×10-2, b2J=2=(0.2±1.4±0.4)×10-2, a3J=2=(1.7±1.4±0.3)×10-2, and b3J=2=(-0.8±1.2±0.2)×10-2. We determine the ratios a2J=1/a2J=2=0.67-0.13+0.19 and a2J=1/b2J=1=-2.27-0.99+0.57, where the theoretical predictions are independent of the charmed quark magnetic moment and are a2J=1/a2J=2=0.676±0.071 and a2J=1/b2J=1=-2.27±0.16.

  2. Multipole study of dispersion and structural losses of photonic crystal fibers

    NASA Astrophysics Data System (ADS)

    Kuhlmey, Boris T.; Renversez, G.; Maystre, Daniel R.; White, T.; McPhedran, Ross C.; Botten, Lindsay C.; de Sterke, Martijn

    2002-04-01

    We describe a multipole theory of photonic crystal or more generally microstructured optical fibers (MOF). We review basic MOF properties such-as losses and number of modes-obtained with our method and expose considerations and results on dispersion management taking into account the losses.

  3. A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank.

    PubMed

    Elking, Dennis M; Perera, Lalith; Duke, Robert; Darden, Thomas; Pedersen, Lee G

    2011-11-30

    A finite field method for calculating spherical tensor molecular polarizability tensors α(lm;l'm') = ∂Δ(lm)/∂ϕ(l'm')* by numerical derivatives of induced molecular multipole Δ(lm) with respect to gradients of electrostatic potential ϕ(l'm')* is described for arbitrary multipole ranks l and l'. Interconversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole-hexadecapole level are calculated for water using the following ab initio methods: Hartree-Fock (HF), Becke three-parameter Lee-Yang-Parr exchange-correlation functional (B3LYP), Møller-Plesset perturbation theory up to second order (MP2), and Coupled Cluster theory with single and double excitations (CCSD). In addition, intermolecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared with ab initio reference values calculated by the Reduced Variation Space method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields. PMID:21915883

  4. A Finite Field Method for Calculating Molecular Polarizability Tensors for Arbitrary Multipole Rank

    PubMed Central

    Elking, Dennis M.; Perera, Lalith; Duke, Robert; Darden, Thomas; Pedersen, Lee G.

    2011-01-01

    A finite field method for calculating spherical tensor molecular polarizability tensors αlm;l′m′ = ∂Δlm/∂ϕl′m′* by numerical derivatives of induced molecular multipole Δlm with respect to gradients of electrostatic potential ϕl′m′* is described for arbitrary multipole ranks l and l′. Inter-conversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole-hexadecapole level are calculated for water at the HF, B3LYP, MP2, and CCSD levels. In addition, inter-molecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared to ab initio reference values calculated by the Reduced Variation Space (RVS) method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields. PMID:21915883

  5. Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms

    SciTech Connect

    Kharchenko, V.F.

    2015-04-15

    The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno–Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determine the polarizability of the atom in excited bound states. - Highlights: • A new description for electric polarization of hydrogen-like atoms. • Expression for multipole polarizabilities in terms of off-shell scattering functions. • Derivation of integral equation determining the off-shell scattering function. • Rigorous analytic solving the integral equations both for ground and excited states. • Study of contributions of virtual multiple scattering to electric polarizabilities.

  6. Identifying the Development in Phase and Amplitude of Dipole and Multipole Radiation

    ERIC Educational Resources Information Center

    Rice, E. M.; Bradshaw, D. S.; Saadi, K.; Andrews, D. L.

    2012-01-01

    The spatial variation in phase and the propagating wave-front of plane wave electromagnetic radiation are widely familiar text-book territory. In contrast, the developing amplitude and phase of radiation emitted by a dipole or multipole source generally receive less attention, despite the prevalence of these systems. There is additional complexity…

  7. Generalized coarse-grained model based on point multipole and Gay-Berne potentials

    NASA Astrophysics Data System (ADS)

    Golubkov, Pavel A.; Ren, Pengyu

    2006-08-01

    This paper presents a general coarse-grained molecular mechanics model based on electric point multipole expansion and Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] potential. Coarse graining of van der Waals potential is achieved by treating molecules as soft uniaxial ellipsoids interacting via a generalized anisotropic Gay-Berne function. The charge distribution is represented by point multipole expansion, including point charge, dipole, and quadrupole moments placed at the center of mass. The Gay-Berne and point multipole potentials are combined in the local reference frame defined by the inertial frame of the all-atom counterpart. The coarse-grained model has been applied to rigid-body molecular dynamics simulations of molecular liquids including benzene and methanol. The computational efficiency is improved by several orders of magnitude, while the results are in reasonable agreement with all-atom models and experimental data. We also discuss the implications of using point multipole for polar molecules capable of hydrogen bonding and the applicability of this model to a broad range of molecular systems including highly charged biopolymers.

  8. Generalized coarse-grained model based on point multipole and Gay-Berne potentials.

    PubMed

    Golubkov, Pavel A; Ren, Pengyu

    2006-08-14

    This paper presents a general coarse-grained molecular mechanics model based on electric point multipole expansion and Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] potential. Coarse graining of van der Waals potential is achieved by treating molecules as soft uniaxial ellipsoids interacting via a generalized anisotropic Gay-Berne function. The charge distribution is represented by point multipole expansion, including point charge, dipole, and quadrupole moments placed at the center of mass. The Gay-Berne and point multipole potentials are combined in the local reference frame defined by the inertial frame of the all-atom counterpart. The coarse-grained model has been applied to rigid-body molecular dynamics simulations of molecular liquids including benzene and methanol. The computational efficiency is improved by several orders of magnitude, while the results are in reasonable agreement with all-atom models and experimental data. We also discuss the implications of using point multipole for polar molecules capable of hydrogen bonding and the applicability of this model to a broad range of molecular systems including highly charged biopolymers. PMID:16942269

  9. Modeling of piezoelectric energy extraction in a thermoacoustic engine with multi-pole time-domain impedance

    NASA Astrophysics Data System (ADS)

    Lin, Jeffrey; Scalo, Carlo; Hesselink, Lambertus

    2015-11-01

    We have carried out the first high-fidelity Navier-Stokes simulation of a complete thermoacoustic engine with piezoelectric energy extraction. The standing-wave thermoacoustic piezoelectric (TAP) engine model comprises a 51 cm long cylindrical resonator, containing a thermoacoustic stack on one end and capped by a PZT-5A piezoelectric diaphragm on the other end, tuned to the frequency of the thermoacoustically-amplified mode (388 Hz). A multi-pole broadband time-domain impedance model has been adopted to accurately simulate the measured electromechanical properties of the piezoelectric diaphragm. Simulations are first carried out from quasi-quiescent conditions to a limit cycle, with varying temperature gradients and stack configurations. Stack geometry and boundary layers are fully resolved. Acoustic energy extraction is then activated, achieving a new limit cycle at lower pressure amplitudes. The scaling of the modeled electrical power output and attainable thermal-to-electric energy conversion efficiencies are discussed. Limitations of extending a quasi-one-dimensional linear approximation based on Rott's theory to a (low amplitude) limit cycle are discussed, as well as nonlinear effects such as thermoacoustic energy transport and viscous dissipation.

  10. Sensitivity analysis in multipole-accelerated panel methods for potential flow

    NASA Technical Reports Server (NTRS)

    Leathrum, James F., Jr.

    1995-01-01

    In the design of an airframe, the effect of changing the geometry on resulting computations is necessary for design optimization. The geometry is defined in terms of a series of design variables, including design variables to define the wing planform, tail, canard, pylon, and nacelle. Design optimization in this research is based on how these design variable affect the potential flow. The potential flow is computed as a function of the geometry and location of a series of panels describing the airframe, which are in turn a function of the design variables. Multipole accelerated panel methods improve the computational complexity of the problem and thus are an attractive approach. To utilize the methods in design optimization, it was necessary to define the appropriate sensitivity derivatives. The overhead incurred from finding the sensitivity derivatives in conjunction with the original computation should be small. This research developed the background for multipole-accelerated panel methods and the framework for finding sensitivity derivatives in the methods. Potential flow panel codes are commonly used for powered-lift aerodynamic predictions for three dimensional geometries. Given an airframe which has been discretized into a series of panels to define the airframe geometry, potential is computed as a function of the influence of all panels on all other panels. This is a computationally intensive problem for which efficient solutions are desired to improve the computational time and to allow greater resolution by use of more panels. One such solution is the use of hierarchical multipole methods which entail approximations of the effects of far-field terms. Hierarchical multipole methods have become prevalent in molecular dynamics and gravitational physics, and have been introduced into the fields of capacitance calculations, computational fluid dynamics, and electromagnetics. The methods utilize multipole expansions to describe the effect of bodies (i